





.HO, 



C 






Paanilkit's Pamtals fax C^acl^trs 

Edited by 

OSCAR BROWNING, M.A., Principal of the Cambridge 

University Day Training College 

AND 

S. S. F. FLETCHER, B.A., Ph.D., Master of Method in the 
Cambridge University Day Training College 



THE LOGICAL BASES 

OF 

EDUCATION 



THE LOGICAL BASES 



OF 



EDUCATION 



BY 

J. WELTON, M.A. 

PROFESSOR OF EDUCATION IN THE UNIVERSITY OF LEEDS 
AUTHOR OF " A MANUAL OF LOGIC," ETC. 



Eontion 
MACMILLAN AND CO., Limited 

NEW YORK : THE MACMILLAN COMPANY 
1904 

All rights reserved 



w^ 



Richard Clay and Sons, Limited, 

bread street hill, e.g., and 

bungay, suffolk. 



First Edition, 1899. 
Reprinted, 1901, 1902 ; Reprinted zuith Corrections, 1904 {tivice). 



/^ J VS 6 






PEEFACE 

The aim of this book is to set forth the rational 
bases of all true educational work. It is believed 
that such bases can only be found in those modern 
developments of logical theory which have marked 
the latter half of this century. Hence, but little of 
the traditional formal logic will be found in the 
book. As a mental discipline I believe that formal 
logic has considerable value, but it seems to me 
certain that we cannot find foundations for modern 
education in a logical theory developed under a. 
conception of knowledge very different from that of 
the present day. 

After the whole of the present book was planned, 
and much of it written, I read in an interesting 
" Review of Educational Currents of Thought in 
1895 in Central Europe," published in the Report of 
the Commissioner of Education, 1896-7, issued by 
the Central Bureau of Education in the United 
States of America, a passage which so exactly ex- 



vi PREFACE 

presses the conception under which I was writing, 
that I venture to quote it : " Logic . . . aims at 
the development of a view by which the world of 
phenomena can be actually understood and the truth 
found. It endeavours to prove that by proper percep- 
tion, consideration, and comparative observation, by 
an arrangement and adjustment under definitions (con- 
sequently by critical judgment and conclusion), and 
by convincing argument and reliable development 
of a scientific system (by means of continued and 
strict induction, deduction, and classification) science 
originates, and a proper view of the world can be 
gained and made perceptible. 

" Such a logic will show how the growing human 
being must be directed so that the physical and 
psychical germs of possibilities of a later develop- 
ment within him may grow towards perfection, and 
that his whole earthly existence may present the 
realization of ethical and aesthetic ideals. It there- 
fore points out the course to be pursued by individual 
training, and outlines the duties of social education, 
which, in its ultimate aims, is more definitely defined 
by ethics. It is the duty of the teacher, therefore, 
to see that upon the foundation of the original work 
of the expounders of this science, a logic be prepared 
in which all useless ballast from formal logic ... is 
omitted, and a scientific methodology (induction, de- 
duction, &c.), be founded on the basis of the qualities 



PREFACE vii 

and laws of human thought which have been made 
objects of perception by psychology. Upon the basis 
of such a logic alone can pedagogy establish the laws 
of intellectual education and found a pedagogical 
methodology" (vol. i., p. 133). 

My experience with the students of the Depart- 
ment for the Training of Teachers at the Yorkshire 
College for the last eight years has convinced me 
that such a treatment of logic appeals to them as 
both helpful and interesting, especially if its reality 
is brought home by the analysis of actual specimens 
of human reasoning such as are given as Exercises 
at the end of this book. 

In such a work as this it would be pedantic to 
attempt to mention all the logicians from whose 
writings I have derived inspiration and suggestion, 
but I cannot refrain from expressing my special 
obligations to Dr. Bosanquet, Dr. Bradley, and Mr. 
Hobhouse. My thanks are due to Mr. W. P. Welpton, 
Lecturer on Education at the York Training Col- 
lege, for his kindness in reading certain portions 
of the book in manuscript and the whole of it in 
proof, and suggesting various improvements. 

J. W. 
Leeds, 
June, 1899. 



TABLE OF CONTENTS 

CHAPTER I 

GENERAL NATURE OF KNOWLEDGE 

PAGE 

5 1. Education and Knowledge 1 

5 2. Knowledge and Truth 1 

3 3. Knowledge and Superstition 2 

I 4. Knowledge and Belief 4 

) 5. Savage Philosophy 7 

I 6. Explanation of the World as a Sum of Things. . 9 

I 7. Explanation of the World by Laws 11 

Factors of Change . 12 

Necessity and Universality of Law .... 14 

Atoms and Energy 15 

I 8. Explanation of the World as System 16 

\ 9. Nature of Reality and of Knowledge 1& 

The Test of Truth 23 

110. The World as Mental Construction 24 



CHAPTER II 

POSTULATES OF KNOWLEDGE 

1. The Factors of Knowledge 27 

2. Postulates of Knowledge 28 

3. The Postulates at the Stage of Sense-perception . 29 

Identity 29 

Contradiction 29 

Excluded Middle 30 

Sufficient Reason 31 



CONTENTS 



PAGE 



4. The Postulates at the Stage of Law 31 

Causation 33 

' Every Event has a Cause ' 34 

' Same Cause, same Effect ' 34 

' Same Effect, same Cause ' 34 

' Cause and Effect equal in Energy ' . . . 36 

Causation and Sequence in Time 36 

5. The Postulates at .the Stage of System ' 38 

Final Causes 39 



CHAPTER III 

KNOWLEDGE AND LANGUAGE 

1. Ideas and I^owledge 42 

i 2. Ideas and Reality 42. 

1 3. Ideas and Images 43 ; 

Thought and Imagination 43 

I 4. Development of Ideas 45 

i 5. Ideas and Language 45 

(6. Language and Communication of Knowledge . . 46 

! 7. Verbal Language 46 

Writing 47 

! 8. Language and Learning 48 

( 9. Spoken and Written Language 49 

510. Meaning and Context 50 

Specific and General Meanings of Words . ■ . 53 

511. Ambiguities of Language 55 

Ambiguities in Individual Words 55 

Ambiguities in Construction 60 

CHAPTER IV 

KNOWLEDGE AND LOGIC 

^ 1. Nature of Logic 62 

5 2, Nature of Judgment 6Si 

^ 3. Judgments and Logic -60 



CONTENTS xi 

PAGE 

§ 4. Abstract Nature of Thought 64 

§ 5. Form and Matter 65 

§ 6. Logic is Abstract and Formal . 66 

§ 7. Function of Logic 67 

§ 8. Value of Logic 68 



CHAPTER V 

NATURE OF JUDGMENT 

§ 1. Judgment and Proposition 69 

§ 2. Judgment and Truth 70 

§ 3. Judgment and Experience 72 

§ 4. Judgment is an Act of both Analysis and 

Synthesis . 73 

§ 5. Subject and Predicate 75 

§ 6. Copula 77 

§ 7. Relative Prominence of Analysis and Synthesis 

in Judgments 78 

§ 8. Summary 78 



CHAPTER VI 

TYPES OF JUDGMENT 

Main Types of Judgment 80 

Development of Judgment 81 

Impersonal Judgments 81 

Demonstrative Judgments 82 

Judgments of Particular Relation .... 82 

Historical Singular Judgments 83 

Enumef ative Judgments 83 

Search for the Universal Judgment .... 84 

The Generic Judgment 85 

The Hypothetical Judgment 85 

Reciprocal Universal Judgments ..... 88 

The Disjunctive Judgment 88 

Negation 91 



ii CONTENTS 

PAGE 

4. Quality and Quantity in Categorical Judgments . 94 

5. Quality and Quantity in Hypothetical and Dis- 

junctive Judgments 96 

CHAPTER VII 

FORMAL RELATIONS OF PROPOSITIONS 

1. The Four-fold Scheme of Propositions 97 

2. Distribution of Terms 98 

3. Conversion 99 

4. Modes of Opposition 101 

Subalternation 101 

Contradiction 102 

Contrariety 102 

Sub-contrariety 103 

Summary of Opposition 103 

CHAPTER VIII 

THE METHOD OF KNOWLEDGE 

1. Truth and Evidence 104 

2. Nature of Method 104 

3. Development of Doctrine of Method 105 

Aristotle , 105 

Mediaeval Logic 105 

Bacon 106 

Newton 107 

Mill 107 

Modern Logic 108 

4. Method and Thought 108 

5. Method and Facts 109 

6. Inferential Character of Method . . ' 110 

7. Characteristics of Methodical Thought Ill 

Purpose Ill 

Definite Starting-point 112 

8. Fallacies incidental to Method 112 

Petitio Prindpii 112 

Ignoratio Elenchi 114 



CONTENTS xiii 

PAGE 

§ 9. Essence of Methodical Process 116 

§10. Nature of Inference 116 

Inference and System 117 

Inference and Previous Knowledge .... 118 

Inference and Universals 119 

§11. Deductive and Inductive Inference 119 

§12. Analysis and Synthesis 121 

§13. Analytic and Synthetic Methods 122 

CHAPTER IX 

DEDUCTIVE INFERENCE 

§ 1. Kinds of Deductive Inference 123 

SYLLOGISM 

§ 2. Nature of Syllogism 124 

Distributed Middle Term 124 

Conclusion warranted by Premises .... 127 

Validity of Syllogism 128 

Minor Rules of Syllogism ........ 129 

§ 3. Forms of Syllogism 129 

§ 4. Hypothetical Syllogisms 130 

CONSTRUCTION 

§ 5. Nature of Construction " 132 

§ 6. Types of Construction 133 

Arithmetical Constructions 133 

Geometrical Constructions 135 

§ 7. Inductive Aspect of Construction 135 

CHAPTER X 

OUTLINE OF INDUCTIVE METHOD 

§ 1. Meaning of ' Induction ' 136 

§ 2. General Method of Induction 137 

§ 3. Direct and Indirect Testing of Hypotheses ... 138 



xiv COKTENTS 

CHAPTER XI 

OBSERVATION 

PAGE 

§ 1. Importance of Observation 140 

§ 2. Liability of Observation to Error 140 

§ 3. Dependence of Observation on Previous Knowledge 141 

§ 4. Observation and Inference 142 

Selection 142 

Recognition 143 

Distinction between ' Observation ' and 

' Inference ' 147 

§ 5. Observation and Prejudice 149 

§ 6. Observation and Scientific Instruments 150 

§ 7. Experiment 150 

CHAPTER XII 

TESTIMONY 

§ 1. Necessity of Testimony 153 

§ 2. Reception of Testimony 154 

§ 3. Tests of Testimony 155 

Good Faith 156 

Accuracy 158 

§ 4. Anonymous Testimony 160 

§ 5. Corroboration of Testimony 162 

Tradition 163 

Independent Corroboration 164 

§ 6. Inference from Absence of Testimony 164 

CHAPTER XIII 

HYPOTHESES 

§ 1. Nature of Hypotheses 166 

§ 2. Origin of Hypotheses 167 

§ 3. Hypotheses and Facts 168 

Danger of Bias 170 



CONTENTS XV 

PAGE 

§ 4. Testing of Hypotheses 171 

§ 5. Descriptive and Working Hypotheses 172 

§ 6. Permissible Hypotheses 173 

8 7. Crucial Instances 174 



CHAPTER XIV 

DIRECT DEVELOPMENT OF HYPOTHESES 

1. Accidental Coincidences and Necessary Connexions 177 

2. Empirical Generalization and Enumerative In- 

duction 178 

3. Analogy 180 

4. Nature of Direct Methods in Induction 184 

5. Method of Agreement . 188 

6. Method of Exclusions 191 

7. Method of Difference 192 

8. Method of Concomitant Variations 195 

9. Method of Residues 200 

10. Example of Use of Methods : Colour of Animals . 200 



CHAPTER XV 

INDIRECT VERIFICATION OF HYPOTHESES 



1. Relation of Indirect to Direct Methods 204 

2. Initial Use of Indirect Method 205 

Circumstantial Evidence 206 

3. The Indirect Method in History . 207 

4. The Indirect Method in Geology and Biology . . 208 

5. Establishment of the Theory of Gravitation . . . 213 

Empirical Laws of Falling Bodies 213 

Empirical Laws of Planetary Motion . . . 214 

Gravitation applied to Moon 215 

Gravitation extended to Planetary Motion 216 
Gravitation extended to all Particles of 

Matter 217 



xvi CONTENTS 

CHAPTER XVI 

DEFINITION, CLASSIFICATION, AND EXPLANATION 

PAGE 

§ 1. Aim of Methods of Knowledge 220 

§ 2. Development of Definition 221 

§ 3. Nature of Definition 223 

§ 4. Definition and other Modes of Stating Meaning . 226 

§ 5. Limits of Definition 229 

Meaning of Proper Names 230 

§ 6. Rules of Definition 231 

§ 7. Nature of Classification 234 

§ 8. Rules of Classification . . . ^ 235 

§ 9. Classification and Definition 235 

Classification and Partition 237 

§10. Disjunctive Classification 238 

§11. Subsumptive Classification 238 

§12. Provisional Character of Classification and Defini- 
tion 241 

§13. Classification and Explanation 242 

§14. Limits of Explanation 244 

§15. Logical Explanation and Familiarization .... 244 

CHAPTER XVII 

LOGIC AND EDUCATION 

§ 1. General Relation of Logic to Education .... 246 

§ 2. Education Relative to Society 249 

§ 3. Method and Self -Activity 252 

Method not Mechanical 253 

§ 4. Educational Method Relative to Current Concep- 
tion of Knowledge 255 

Heuristic Methods 255 

§ 5. Method of Science and Method of Education . . 257 

§ 6. Maxims of Method 261 

EXERCISES IN INFERENCE 266 

INDEX 281 



THE LOGICAL BASES OF 
EDUCATION. 



CHAPTER I 



GENERAL NATURE OF KNOWLEDGE 



§ 1. — Bacon begins one of the best-known of his Education 
essays with the words: "'What is truth?' said Knowledge. 
jesting Pilate j and would not stay for an answer." 
Whether or not this is a libel on the Roman pro- 
curator, it certainly represents a mental attitude 
which cannot be adopted by the educator. One of 
the main parts of his work is teaching. And 
teaching has a two-fold aspect — on the one hand it 
regards the pupil, and on the other it regards the 
subject taught. Between these two it tries to 
establish the relation we call knowledge. The aim 
of teaching is, then, to lead the pupil to attain 
knowledge, and to develop in him the power of 
using and extending that knowledge. 

§ 2. — Now, if we ask ourselves what we mean by Knowledge 
* knowledge ' we can find no other answer than that ^^^ Truth. 

IE ij 



2 THE LOGICAL BASES OF EDUCATION chap. 

it is that part of human thought which is proved 
true. And human thought is true just so far as it 
agrees with the facts of the world. All knowledge 
is, then, a grasp of truth. Not indeed of the whole 
truth : that we do not know, and never shall know. 
For the whole truth is the totality of reality or 
existence ; in other words, the universe. As this is 
infinite it can never be grasped by the finite human 
intelligence. But, as generations succeed each other, 
knowledge advances. Taking each new position as 
a fresh starting point, man uses the knowledge he 
has acquired as a key to unlock fresh mysteries. 
What was so wonderful to our forefathers that it 
could only be accounted for by the assumption of 
supernatural agency is regarded by us as common- 
place. Thus the bounds of superstition are con- 
tinually contracted. For superstition has play only 
where knowledge is absent and fancy takes its place. 
As Mr. Clodd remarks, " magic rules the life of 
the savage," ^ whilst the life of civilized man tends to 
become more and more completely ruled by a 
rational conception of law and system. 
Knowledge § 3 . — The thought of the modern civilized European 
sSpsrsti- is then, especially at first sight, very different from 
tion. that of the savage. But this must not blind us to 

the fact that there is continuity between them ; that 
the former has been evolved slowly and with difficulty 
from the latter. " The low intellectual environment 
of man's barbaric past was constant in his history for 
thousands of years." ^ It was only when man began 
to think and enquire, as well as to feel and fancy, 
that knowledge began to take the place of belief in 
magic, in charms, in fairies, and in all the other 
apparatus by which savage man attempts to explain 

^ Tom Tit Tot, p. 51. 
2 Clodd, op. cit., p. 106. 



GENERAL NATURE OF KNOWLEDGE 3 

the phenomena he sees about him. For modern 
Europe this birth of thought took place in Greece 
less than three thousand years ago. Since then 
there has been gradual advance, not however without 
long periods of stagnation, and even of retrogression. 
We need not go back very far to find superstition 
governing most of the life of the majority of English- 
men. King James I. believed firmly in magic, and 
in his book on Doemonology, he speaks of the " devil 
teaching how to make pictures of wax or clay, that 
by roasting thereof the persons that they bear the 
name of may be continually melted or dried away by 
sickness." And James was "the British Solomon." 
Indeed, we need not leave our own day to find many 
examples of the truth that whenever knowledge is 
absent superstition reigns. The thorough-going con- 
ception of the universality of natural law exists amongst 
comparatively few even in our own day. " Scratch 
the epiderm of the civilized man, and the barbarian 
is found -in the derm " says Mr. Clodd with undeni- 
able truth. " In proof of which," he goes on, " there 
are more people who believe in Zadkiel's Vox 
Stellarum than in the Nautical A Imanac ; and rare 
are the households where the Book of Dreams and 
Fortune-Teller are not to be found in the kitchen." ^ 
And again : " As many a stable-door and mainmast 
testify, the nailing of horse shoes to ' keep off the 
pixies,' and, conversely, to bring luck to farmer and 
sailor, thrives to this day." 2 Many other examples 
are given by Mr. Clodd in the very interesting book 
from which we have quoted, and doubtless, every 
reader will be able to furnish additional instances. 
But enough has been said to illustrate the point that 
the outcome of ignorance is superstition. 

Now, it should be noted that superstitions have 
^ Op. cit., p. 97. 2 ii^i^^^ ^ 34^ 

B 2 



4 THE LOGICAL BASES OF EDUCATION chap. 

their origin mainly in man's feelings and emotions, 
and especially in the emotion of fear, for the 
unknown generally inspires terror in a mmd that 
has little or no conception of natural law. But 
superstitions are not merely mental errors, they have 
a practical bearing, for, in so far as they are believed, 
they determine conduct. 

Further, what has been said has made it evident 
that the only cure for superstition is increased know- 
ledo-e. And this has a deep interest for the 
educator ; for, again to quote Mr. Clodd, " the art 
of life largely consists in that control of the emotions, 
and that diversion of them into wholesome channels, 
which the intellect, braced with the latest knowledge 
and with freedom in the apphcation of it, can alone 

effect."! ^^ . ^ 

§ 4.— The above remarks have brought into 
prominence several important points which we shall 
do well to consider. In the first place we see that 
all belief is not knowledge. Belief is unquestioning 
acceptance by the mind. But the savage beheves as 
firmly in various forms of magic as the civilized man 
does in the law of gravitation. And his beliefs 
influence his actions. " The Basuto avoids the river- 
bank, lest, as his shadow falls on the water, a^ 
crocodile may seize it, and harm the owner . . . 
the Arabs believe that if a hyena treads on a shadow, 
it deprives the man of the power of speech." Now 
it may seem strange that such beliefs have been able 
to survive for so many generations the continual 
contradictions they must have received from experi- 
ence. Indeed, this would be inexplicable were it 
not for another piece of experience— the fact of the 
marked conservatism which human nature shows 
with regard to its beliefs. Prejudice is an enormous 
? Op. a7., p. 109. ' mU, pp. 79-80. 



1 GENERAL NATURE OF KNOWLEDGE 5 

force in human life, and not less potent is that 
mental inertia which makes it hard for men to strike 
out a new line of thought for themselves. "It is 
not error," wrote Turgot, " which opposes the pro- 
gress of truth ; it is indolence, obstinacy, the spirit 
of routine, everything that favours inaction." ^ It is 
only when this mental indolence is overcome, when 
the spirit of enquiry is roused, that men begin to 
ask why they believe this or that, and according to 
the answer to retain or reject the belief. 

This leads us to see both the difference and the 
connexion between belief and knowledge. So far as 
the mental state of any individual is concerned, 
belief and knowledge are so far alike that both are 
states of full assurance of the truth of the matter in 
question. But they differ in this — that in the case 
of knowledge alone this assurance can be shown to 
be justified by evidence other than itself. For ex- 
ample a savage believes that an earthquake is the mark 
of the anger of some supernatural being with those 
who suffer its effects, but he can bring forward no 
evidence outside the earthquake itself to support his 
belief. On the other hand, the modern scientific 
man can show by unimpeachable evidence that the 
earthquake is the result of natural laws and is itself 
an expression of the orderly working of the universe. 
In thus relating the earthquake to other physical 
events he has replaced what was mere belief by 
knowledge. 

There is a further and most important distinction. 
Belief is always an individual act. Any number of 
persons may, indeed, agree in believing the same 
thing, and this we loosely call " sharing a belief " or 
"holding a common faith." But the belief is not 
common if we use our words strictly. What is 
1 Quoted by Mr. Clodd, oj). cit., p. 108. 



6 THE LOGICAL iBASES OF EDUCATION chap. 

common is the object of belief : each man believes 
for himself, each man feels his own full assurance. 
And this assurance he cannot communicate to 
another. The utmost he can do is to influence the 
mind of him whom he wishes to convert so as to 
incline him to accept the same object of belief. 
Belief is then, in its very essence, particular ; that is, 
it is the state of some one individual mind. Know- 
ledge, on the other hand, is universal; that is, 
it is common to any number of minds. This is 
because knowledge is, as has been already said, a 
grasp of truth, or, as we may put it in other 
words, an insight into some portion of reality. It 
follows that knowledge is not dependent on any one 
individual mind, for neither the belief nor the 
thought of any individual can alter an element of 
the real world. It is true that knowledge is 
increased by the work of individual minds. >But once 
a piece of knowledge is arrived at it can be com- 
municated to others and made common property. 
This is so because the evidence which establishes 
every piece of knowledge can be made clear. Of 
course, when a piece of knowledge is grasped by 
an individual mind, ifc is believed, and it becomes 
parb of the contents of that mind ; the act ci 
knowing is thus individual. But whilst belief is 
nothing beyond the act of believing, knowledge 
is not the mere act of knowing. For nothing is 
knowledge which is not based on evidence sufiicient 
to prove it, that is, which is not shown to be part of 
the order of the world. Any mind which can 
appreciate this evidence is forced to accept the piece 
of knowledge which is thus substantiated. Hence, 
all knowledge is in its very essence universal in its 
nature ; for all minds which can understand it must 
accept it as something not merely believed but 



I GENERAL NATURE OF KNOWLEDGE 7 

as actually proved, and therefore known to be 
true. 

This fact that all knowledge is of the truth, whilst 
belief is frequently of the false, leads us to see that the 
general conditions of knowledge are independent of in- 
dividual beliefs. Men have, indeed, often believed they 
possessed knowledge when future advances have shown 
that their supposed knowledge was imperfect or 
even false. Such a mistake is easily understood when 
it is borne in mind that to the individual both 
knowledge and belief are states of full assurance ; 
that all knowledge is belief, though all belief is not 
knowledge. It is easy, then, for a man to deceive 
himself as to the extent to which his beliefs are really 
supported by sufficient evidence, and especially so 
since even his power to appreciate the weight of 
evidence is partly dependent on the amount of his 
knowledge. He may, then, easily confuse considera- 
tions which appeal to his prejudices and agree with 
his beliefs with true evidence which appeals only to 
his reason. Such considerations help us to see that 
whenever wdiat is not true has been mistaken for 
knowledge the reason has been that the real condi- 
tions of knowing have been departed from. When 
these conditions are really fulfilled, knowledge results. 
It will be our task in this book to examine the nature 
of these conditions. 

§ 5 — A second point brought out by the compari- Sayage 
son of the thought of savages with that of civilized ^ ^ ^^'^^ ^' 
man is that at all times man tries to find some 
explanation of the world in which he lives. At every 
moment of his life he is brought into contact with 
objects and phenomena over which his wishes and 
feelings and thoughts have no control. The storm 
comes and sweeps away his hut, the sun rises and sets, 
the moon waxes and wanes, the clouds gather and 



8 THE LOGICAL BASES OF EDUCATION chap. 

disappear. Or again, his own actions frequently 
have results which he neither forsees nor desires. 
He eats a new berry and is ill. He steps on a 
stone in climbing a hill ; it gives way under him, 
he falls and is injured. Even consequences which 
he can foresee, in many cases he cannot prevent. 
He fails to find water and suifers thirst ; he is 
overtaken by the prairie fire and is burnt. 

Thus even at the lowest stage of development man 
cannot help finding himself in the midst of a world 
of which he forms a part, but which exists independ- 
ently of him. But the savage has not in the strict 
sense of the word begun to think. He is too fully 
occupied in keeping himself alive to concern himself 
with anything which has not a direct personal 
bearing. Especially must he be continually on guard 
against agencies that may work him ill. He is 
always finding new sources of evil to himself, and he 
is inclined to suspect the unknown. Savage man 
thus never looks at his world as a whole. Eor him 
it consists of isolated things and events which have a 
bearing — generally evil — on his own life and his own 
comfort. The most obvious explanation which 
occurs to him is to attribute to all things those 
powers of life which he himself possesses. Every 
thing is alive, or is at least the abode of a living 
spirit, generally of a malignant nature. Hence 
arises, that general belief in magic which marks all 
races of savages. 

So, too, savage man has not learnt to distinguish 
between realities and symbols. Nothing is con- 
nected with a man more uniformly than his shadow ; 
hence it is believed that a man may be injured 
by doing to his shadow what would injure the man 
if done to himself. Similarly a man's name is 
believed to be an integral part of himself, and it is a 



[ GENERAL NATURE OF KNOWLEDGE 9 

universal belief amongst savages that if an enemy 
knows a man's name he has him in his power. 
Consequently, in many tribes the real names are 
kept secret and every individual is known by a 
nickname. 

These few examples warn us against expecting 
to find any consistency in the philosophy of the 
savage. He attempts to explain his world not as a 
whole but piece by piece. He has hardly indeed 
begun even to ask himself what these separate 
objects of his experience are ; of their real properties 
he is profoundly ignorant. Still, he has begun to 
see, though most dimly, that there are relations 
between things. It is true that the only relations 
he founds his attempts at explanation upon are those 
of striking, but often very superficial, resemblance. 
Yet it is in this vague and fragmentary recognition 
of relations that science has its root. 

§ 6. — As man begins slowly to emerge from Expiana- 
savagery less and less of his time and energy is wSid^a?^ 
occupied with the mere preservation of his life. So ^^.^^^ °^ 
he begins to find time to feel curiosity about those 
things which do not immediately affect him, and 
even about the world as a whole. But the 
influence of the traditional beliefs remains strong. 
He still regards himself as the centre of the universe, 
the being for whose benefit sun, moon, stars and 
earth were made. Consistently Avith this he still 
thinks of ' things ' — i.e. material objects which can 
affect him through his senses — as independent 
pieces of reality whose nature is not affected by the 
relations in which they stand to each other. In 
other words, he regards the world as a sum of things 
whose relations with each other are accidental. 
From this point of view ' things ' are units of exist- 
ence which can be re-arranged in any way, like a set 



10 THE LOGICAL BASES OF EDUCATION chap. 

of ninepins or a group of billiard balls, without 
altering their nature. 

Within such a philosophy there is still abundant 
room for magic and supernatural agencies. For 
whilst the relations between things are regarded as 
indifferent and variable in any way without affecting 
the nature of the things related, it is obvious that 
those relations will not be carefully investigated, 
and the analogy of a living agent will still be con- 
tinually called in to explain occurrences which are 
not understood. So fairies and witches remain part 
of the machinery of the world, and means must be 
taken to guard against their evil influence. Hence 
the survival of the use of charms, which is still 
extremely common amongst the majority of the 
people of Western Europe. " Many a fragment of 
cabalistic writing is cherished and concealed about 
their persons by the rustics of Western Europe as 
safeguards against black magic." ^ 

Again, so long as the relations of things are not 
regarded as important to the constitution of reality, 
and so remain unstudied, relations of striking like- 
ness will continue to exercise undue influence over 
man's attempts at explanation. Thus, " doctors in the 
seventeenth century . . . with . . .perchance unconscious 
humour, gave their patients pulverized mummy to 
prolong their years. ' Mummie,' says Sir Thomas 
Browne, ' is become merchandise. Mizraim cures 
wounds, and Pharaoh is sold for balsams.' " ^ Even 
in the present day " in Suffolk and other parts of 
these islands, a common remedy for warts is to 
secretly pierce a snail or ' dodman '-Avith a gooseberry- 
bush thorn, rub the snail on the wart, and then 
bury it, so that, as it decays, the wart may wither 

^ Clodd, op. cit., pp. 2U— 215. 
2 Thirl, pp. 62—6.3. 



I GENERAL NATURE OF KNOWLEDGE 11 

away." ^ This is quite on a level with the action of 
the Cheroki Indians when " to ensure a fine voice, 
they boil crickets and drink the liquor." ^ 

§ 7. — Insufficient as is the explanation of the Expiana- 
world which sees in it only a sum of things which woJid by ^ 
may enter into any relations with each other without ^^^^• 
affecting their own nature, it yet satisfied the mind 
of man till a few centuries ago. It was only with the 
birth of modern physical science that men really 
began to appreciate the importance of relations in the 
constitution of the world. But the old view of the 
independence of things still remains the philosophy 
of all the uneducated — that is, of all young children 
and of the great majority of adults. And it is from 
that view the educator must start in leading his 
pupils to a truer conception of the world. In this 
respect, as in so many others, the child epitomizes 
the evolution of the race. 

It may be said, then, that modern science began 
with the discovery that the nature of things is 
affected by their relations. And this discovery was the 
necessary result of a deeper study of things themselves. 
Even to a superficial observation it was evident that 
many things change according to the relations 
in which they are placed. The clouds are 
scattered by the wind, the snow melts in the 
sun. With other things, indeed, the case seemed 
different, and in nothing was stability more 
apparent than in " the everlasting hills." But closer 
observation showed that even these changed contin- 
uously. Rain and frost, torrent and glacier were 
always at work, and their effects could be seen by the 
careful watcher. Thus, the idea that change is the 
characteristic of all things, and not a mere accident to 
some, began to take firmer and firmer hold of men's 
1 Op. cit., p. 62. 2 j^^-^ 



12 THE LOGICAL BASES OF EDUCATION chap. 

minds, though doubtless it was long before the stage 
was reached which is expressed in Tennyson's lines, 

" The hills are shadows and they flow 
From form to form and nothing stands ; 
They melt like mist, the solid lands, 
Like clouds they shape themselves and go ! " ^ 

Factors of But change implies an agency which causes the 
change. Either this agency is to be found in the 
nature of the thing itself, in some other thing in 
active relation to it, or in a combination of the two. 
Now, the agency of things from without is in many 
cases obvious. Trees and land are washed away by a 
torrent, smiling fields and prosperous cities are over- 
whelmed by a volcanic eruption, fire burns and water 
drowns. Hence, agency from without has seemed to 
some a sufficient explanation of all change. In this 
too we find the survival of the older belief, though 
under a new aspect. The older belief regarded things 
as essentially stable, and all change as accidental 
and exceptional to the general order. When 
change was observed it was attributed to external 
agency. The newer view was in opposition to 
this in regarding change as the normal state, but it 
agreed with it in attributing all change to outside 
agency, though the agency sought was that of material 
things instead of that of supernatural beings and 
unknown powers. 

Such a view, however, cannot survive deeper 
critical examination. External influences are soon 
seen not to be the only determining factors. An 
acorn and a grain of corn may be planted side by 
side and exposed to the same influences of soil and 
weather, but the one will develop into an ear of 
corn and the other into an oak tree. It is true that 

^ In Memoriam, cxxiii. 



I GENERAL NATURE OF KNOWLEDGE 13 

neither will develop at all apart from appropriate 
conditions of soil and climate, and so their develop- 
ment is determined by those external conditions. 
But it is equally clear that, given the conditions, the 
development which actually takes place is determined 
by the thing's own nature. And this nature is the 
essence of the thing itself. External conditions are, 
then, contributing factors in development, but they 
alone do not determine the nature of that develop- 
ment. A plant's life-history can be understood only 
when both its inner nature and its surroundings are 
taken into account. 

In the animal world the same thing is yet more 
manifest. An animal is much more independent of 
external conditions than is a plant, for by changing 
his locality he may seek conditions which suit him. 
To the extent to which he can do this he determines 
his conditions rather than is determined by them. 
Doubtless the latter factor in his life is not absent, 
and in the course of ages may profoundly modify his 
constitution. But the mere influence of surround- 
ings will not account for the whole of animal life. 

In the highest degree of all is this self-determina- 
tion seen in man, who, by the exercise of his reason 
and will, can modify his environment in all kinds of 
ways. What a man does and becomes is, of course, 
influenced by circumstances external to himself, and 
that often in a very great degree. But his conduct 
and life are not absolutely determined by those 
circumstances, but are regulated by the man's own 
nature. 

Even in the inorganic world the same thing is 
seen. Soil is washed away by a torrent, but both 
the extent and the mode of the denudation are de- 
termined by the nature of the soil itself as well as 
by the character of the torrent. Many solids melt 



14 THE LOGICAL BASES OF EDUCATION chap. 

when exposed to heat ; but whilst wax liquefies at 
65° C, lead remains solid till 335° C. is reached, and 
iron only leaves the solid state at a temperature of 
1200° C. 

Throughout then, it is seen that all change in 
any object whatever is determined both from within 
and from without. The extent and time of the 
change are mainly determined by action from with- 
out, but its character is, at any rate partially, 
determined by the inner nature of the thing. 
Necessity It is Only when this is fully grasped that the 
versaiity Conception arises that every change which takes 
of Law. place is necessary. And by ' necessary ' is meant that 
given such a thing under such conditions, such a 
change must take place. This is the conception of the 
universality of law which marks modern scientific 
thought. We are apt to under-estimate the scope of 
this principle. As Professor Huxley put it : " Even 
thoughtful men usually receive with surprise the 
suggestion, that the form of the curl of every wave 
that breaks, wind-driven, on the sea-shore, and the 
direction of every particle of foam that flies before 
the gale, are the exact effects of definite causes ; and 
as such must be capable of being determined, de- 
ductively, from the laws of motion and the properties 
of air and water." ^ Such an example shows how 
limited our knowledge really is. It is mainly 
under the pressure of some practical interest that 
men strive to extend their knowledge. And so 
it is only about a few classes of things and events 
that men consider it worth their while to think 
accurately — that is, to think truly, or to know. 
But accurate thought is scientific thought. We are 
apt to suppose that nothing belongs to science except 
those fev/ phenomena about which men do try to think 
^ Hume, p. 122, 



GENERAL NATURE OF KNOWLEDGE 15 

accurately. But the scope of science is the scope of 
the possibility of knowledge. As the late Professor 
Clifford said : " Scientific thought does not mean 
thought about scientific subjects with long names. 
There are no scientific subjects. The subject of 
science is the human universe ; that is to say, every- 
thing, which is, or has been, or may be related to 
man." ^ 

The scientific conception of the universality of law Atoms and 
is, then, an attempt to explain everything which ^"'''^^" 
happens in the universe by the relations involved. 
If these are made clear, then, assuming that the 
nature of the 'things' related remains constant, 
any change is so far accounted for that it is shown 
to be consistent with what is already known of the 
action of thing on thing. But modern physics goes 
further and tries to explain the nature of the 
'things' of ordinary life— the animal, the plant, 
the rock, the water— on the same principle. It 
seeks " the final constituents of the physical world 
in countless atoms, invisible from their minuteness, 
persistent in their duration, and unchangeable in 
their properties. These atoms .... produce by 
the variety of their positions and motions the 
different kinds of natural products and their change- 
ful development." 2 The atom, then, is assumed "to 
have no positive quality of its own to produce change 
—it simply persists unchanged as a centre of the 
action and reaction of forces. Change is thus the 
result of energy ; it is only a rearrangement of the 
forces centred round the atom. Hence, the ultimate 
reality of the universe is found in energy, and this 
mechanical explanation of the world assumes its 
most developed form in the doctrine of the con- 

^ Essays, p. 86. 

^ Lotze, Microcosmus, vol i, pp. 31—33, 



16 THE LOGICAL BASES OF EDUCATION chap. 

servation of energy. This theory is certainly simple, 
but, as an ultimate and complete explanation of 
reality, it is inadequate. It does not fully explain 
the whole of the phenomena of the inorganic world, 
whilst it is quite unable to deal with the phenomena 
of life, especially with those of development. 
Bxpiana- § 8. — But even were this not the case, the 

w?rM a? ' mechanical theory does not give an ultimate resting- 
System. pig^^e for thought. For it looks upon everything 
which exists as dependent on its relations to some- 
thing else. Now, if a phenomenon A is explained as 
due to the combination of B and C in a customary 
relation X, yet B, C, and X equally need explanation, 
and so with the factors which compose their causes. 
Thus we are driven into a series of explanations 
by relations which can never come to an end. 
Again, we must remember that when we speak ^ of 
an* event or a change, we are arbitrarily separating 
in thought one little piece of the world process which 
is not so separate in reahty. As Mach puts it : 
" There is no cause nor effect in nature ; nature has 
but an individual existence ; nature simply is" ^ By 
nature here is meant the universe as a whole. That 
cannot be explained by its relations to anything else, 
for there is nothing else. This leads us to pass fr-^m 
the scientific to the philosophic stage of interpreta- 
tion. The essence of this is that it regards the 
universe as a system whose changes are due to its 
own inherent activity. But the only self -originating 
activity we can conceive is that of thought and will ; 
that is, of rational will. We are then compelled, if we 
push our search for explanation as far as it will go, 
to find in the universe the expression of the rational 
activity of an Absolute Being who includes all 
existence. Here, however, we have stepped beyond 
1 Science of Mechanics, p. 483, 



GENERAL NATURE OF KNOWLEDGE 17 

the bounds of science into philosophy. As Dr. Merz 
says : " Science will not teach us to understand 
nature and life .... it is the philosophical or 
religious problem." ^ But it is only when the inter- 
mediate or scientific stage has been passed through, 
and this ultimate stage reached, that education can 
be said to have accomplished its work. A conception 
of the necessary order of development such as we 
are sketching, is, therefore, a part of the essential 
equipment of the educator. 

The idea of system is partially recognized in the 
scientific view. For according to it the universe is 
no longer looked upon as a sum of independent units, 
as in the interpretation of sense-perception, but as 
composed of parts in essential relation to each other. 
The philosophic view simply completes this idea of 
system and makes it the basis of all interpretation, 
and in doing so it takes up into itself what is true 
in each of the preceding modes of interpretation. 
It will be well, then, to consider briefly what is really 
meant by a ' system.' Let us do this by taking a piece 
of machinery, say a watch, as an illustration. The 
watch consists of various wheels, springs, and other 
^-Ivorks ' ; but these do not constitute a watch unless 
they are arranged in a certain definite way. The 
watch is, therefore, not merely the complete sum of 
its parts ; there is no watch unless those parts are in 
certain relations to each other. Further, the mean- 
ing of each part depends on those relations ; for its 
meaning is the share it plays in that work of measur- 
ing time for which the watch exists. But this share 
it is only able to perform through the action upon it 
of the other parts of the watch. A knowledge of its 
relations to those other parts will, then, enable us to 

^ History of European Thought in the mneteenth Century, 
vol. 1., p. 383. "^' 



18 THE LOGICAL BASES OF EDUCATION chap. 

understand how the part in question does its work. 
An insight into why that work is done involves 
however, a knowledge of the purpose for v/hich the 
whole watch exists and of the relation of the activity 
of this part to the total activity by which that 
purpose is carried out. A complete comprehension, 
then, of any one part of such a system involves 
a knowledge of the relations of that part to 
every other part, and to the whole. Of course, 
these relations are of very different degrees of 
directness. But in a system there is no break, 
and therefore every part is connected, directly or 
indirectly, with every other part. Complete know- 
ledge of any one part would include knowledge 
of all its relations — direct and indirect — and would, 
consequently, be knowledge of the whole. Of a small 
and artificial system like that of a watch such 
complete knowledge is attainable, but the wider and 
more complex a system is, the more difficult it becomes 
to reach such perfection of knowledge. Still the 
characteristic features of a system are the same, no 
matter what its extent and complexity. The scien- 
tific view then, by insisting on the essential part 
played by relations in the universe, begins to regard 
it as a system. The philosophical view by emphasiz- 
ing the essential relation of each part to the whole, 
that is, the purpose or function of each part with 
respect to the whole, as that in which alone com- 
plete explanation can be found, develops and com- 
pletes this conception. 

Of this system of the universe the total knowledge 
of mankind is very imperfect. Still more imperfect 
is the knowledge of each individual man, for meagre 
as is the total knowledge of the race it is yet so ex- 
tensive as compared with the limited capacities of 
each individual that no one can master more than a 



I GENERAL NATURE OF KNOWLEDGE 19 

small portion of it. Hence we have specia-lists ; that 
is, the totality of the field of knowledge is divided 
up into sections, and each thinker confines his 
efibrts to a more or less limited section. These 
sections, which we are accustomed somewhat loosely 
to regard and speak of as separate ' sciences,' are 
more or less fully organized systems in themselves, 
and they are in turn divided by us into smaller 
constituent systems. The conception of system, 
therefore, determines all man's attempts at organizing 
knowledge. We have a countless number of small 
systems, themselves constituents of larger systems, 
and so on till we reach the all-embracing system of 
the universe itself. And throughout all there is 
continuity of relation, so that even the smallest 
thing — a grain of dust or a passing whim — is in 
essential connexion with every other part and with 
the whole. As Tennyson beautifully says — 

" Flower in the crannied wall, 
I pluck you out of the crannies, 
I hold you here, root and all, in my hand, 
Little flower — but if I could understand 
What you are, root and all, and all in all, 
I should know what God and man is." 

§ 9. — But it may be asked "In what sense can Nature of 
this ultimate stage be called knowledge ? Is it not 2fd^o? 
rather a piece of philosophical imagination or of Knowledge. 
religious faith 1 " To answer this question we must 
investigate somewhat more fully the nature of 
knowledge. 

Knowledge, as has been said, is an insight into 
the nature of reality. In other words, the object 
of knowledge is always some portion of that real 
world of which we ourselves form a part. Now we 
are brought into contact with reality in every 
piece of sense-experience. We look, and what we 

c 2 



20 THE LOGICAL BASES OF EDUCATION chap. 

see is independent of our wish ; we listen, and cannot 
determine what we shall hear ; we touch, but the 
surface touched is not influenced by our desires ; 
we taste and smell, but the resulting sensation is 
due to the object tasted or smelled. In a word, 
what we perceive is given us, is determined for 
us by the nature of the real world. Thus, reality con- 
strains us, and it is this constraining power which 
marks off reality from fancy. But reality is not 
simply what we experience through our senses here 
and now. We find the same constraint in memory. 
We can recall our past doings and experiences, and 
much as we may wish them different from what 
they were, we cannot believe them different. 
They also are part of our reality. They form our 
real past, which is often as different as possible from 
the past we like to fanc}^. This same constraint is 
not felt as regards the future. That, indeed, we can 
often anticipate, but we know the anticipation is only 
more or less probable, it is never absolutely certain 
as is the past. 

But neither present sense-experience nor memory 
of the past does more than put us in touch with 
reality. It gives us the material of knowledge, 
but not knowledge itself. Even in the simplest 
case, what is given to the senses has to be inter- 
preted by thought. I see a yellow sphere of two or 
three inches diameter and I recognize it as an orange, 
and acting on this recognition I attribute to it 
many qualities and relations other than those now 
present to my senses. I say it is juicy and the fruit 
of a tree which grows in a warm climate. This and 
much more the little yellow sphere means to me. 
But very little of this is directly given in experience. 
Some of the rest has been given in my past e'xperience, 
some I have received on the testimony of others, 



I GENERAL NATURE OF KNOWLEDGE 21 

some I have inferred. Or again, I \\ ake in the morn- 
ing and see the ground covered with snow, whilst my 
memory tells me there was no snow there when I 
went to bed the night before. I feel no hesitation 
in saying the snow has fallen from the clouds during 
the night. But I do not know this by sense-ex- 
perience ; I infer it. No doubt the inference is 
based on past experiences, but it is itself neither 
an experience of the senses nor the memory of .such 
an experience. And, of course, even in explaining 
the white appearance which the ground presents to 
my sight as due to a covering of snow, I am going 
beyond sense-experience in the same way as in the 
case of the orange we have just considered. 

Further, sense-experience leaves many gaps which 
thought must fill up. For example, I left my 
house this morning and returned to it this afternoon. T 
quite expected to find it standing just where and how I 
had left it. But it had not been presented to my 
senses all day, nor had I received the testimony of 
another to whom it had been thus presented. Yet I 
feel no doubt that it continued to exist, for other- 
wise I must assume that it comes into being just as 
some one happens to look at it or touch it, and goes 
out of being immediately it ceases to be perceived. 
But this is unthinkable, for it contradicts the only 
possible explanation of reality. If the existence of 
things were dependent on their perception, then 
obviously they could not compel that perception. 
But this contradiction is, of course, made manifest by 
thought, not by the testimony of the senses indepen- 
dently of thought. 

Hence in every case we see that sense impressions 
have to be interpreted by thought before they can 
have meaning for us, and without meaning they 
cannot enter into knowledge. When so inter 



22 THE LOGICAL BASES OF EDUCATION chap. 

preted we call them 'facts.' A 'fact' then is a 
thing or event interpreted by thought. And this 
interpretation is, speaking broadly, the harmonizing 
the present experience with experiences received in 
the past. 

Such interpretation may, no doubt, be wrong. The 
yellow sphere may be a skilful imitation of an orange, 
and not the fruit itself ; the whiteness of the ground 
may be due to hoar frost, and not to snow. In such 
cases, however, further investigation shows the mis- 
take by bringing to light something inconsistent with 
our suggested explanation. The mock orange con- 
tradicts past experiences of touch and taste ; we find 
appearances in the hoar frost which we do not find 
in snow, or some one who has been out all night 
assures us that no snow has fallen. Truth cannot 
contradict itself ; whenever, therefore, we find con- 
tradiction, we know that we have falsity. All 
thought must postulate this, for, without it, thought 
itself becomes impossible. Thus we do not hesitate 
to reject even personal testimony on the ground that 
it is inco-.sistent with the only explanation which 
will harmonize an enormous number of other experi- 
ences. For example, when " M. Louis de Rougemont " 
asserted that, whilst swimming in the sea ten miles 
from land, he could see the natives " putting out in 
their catamarans to help us," ^ we declined to 
accept the statement as true, on the ground that the 
rotundity of the earth would make the alleged fact 
impossible unless those savages were some sixty-six feet 
in height. No one thought of accepting the writer's 
statement as a disproof of the general theory of the 
shape of the earth, for to do so would have been to 
accept as a fact a contradiction to innumerable other 
facts as to whose reality there can be no doubt. 
1 Wide World Magazine, October, 1898, p. 6. 



1 GENERAL NATURE OF KNOWLEDGE 23 

Of course, it not infrequently happens, as has 
already been said, that what is at one time regarded 
as true is found at a later period to be false. 
This always takes place when some previously un- 
known facts are discovered which are inconsistent 
with the accepted explanation. We continually 
have examples of this in our daily life, and the 
phrase " Ah, that throws a new light on the matter 1 " 
indicates that the explanation which had hitherto 
been satisfactory to us, as harmonizing all the facts 
known, is now, by the knowledge of other facts 
inconsistent with it, found wanting. Yf e must then 
seek a new explanation which will find a place for 
these new facts as well as for those formerly known. 
In the history of the world's thought probably the 
most striking example of this was the substitution of 
the theory that the sun is the centre of the planetary 
system for the theory that the earth holds that posi- 
tion. Here also it was the discovery of new facts 
which made the old theory untenable, though it had 
for centuries sufficed to harmonize all that was known 
of the motions of the heavenly bodies. 

It appears, then, that consistency with all other The Test 
knowledge is the test of truth, and it follows that, as 
knowledge is always advancing, it is often impossible 
to say with absolute assurance that any particular 
item of our interpretation of the world is true. 
Further knowledge may, in many cases, necessitate 
a revision of such interpretations in the future as in 
the past. 

As knowledge grows, however, the amount of fully 
established truth is gradually increased. An item 
of interpretation must be held to be absolutely estab- 
lished as true whenever it is the only possible 
explanation of the facts. If the ground is covered 
with snow, snow must have fallen from the clouds. 



of Truth. 



24 THE LOGICAL BASES OF EDUCATION chap. 

Similarly, the assumption of the continuous existence 
of material objects independently of our perception 
of them is the only possible way of bringing con- 
sistency into our experience. Whenever, then, an 
explanation is ' necessary,' in the sense that to refuse 
to accept it would be to introduce contradiction into 
the thought and experience of mankind, that ex- 
planation is as much a part of knowledge as is the 
actual experience to which it gives meaning. 

It is in these considerations that we find the 
answer to the question with which we began this 
section. It is in this sense of necessary explanation 
that we hold the theory that the universe is a 
self-determined system — the expression of a rational 
activity which manifests itself in all the changes 
which are, or ever have been, or ever will be — to be a 
matter of knowledge. It is the only interpretation 
which can harmonize the thought and experiences of 
mankind, and give a firm basis to knowledge- 
Moreover, the very fact that we can interpret the 
world and give a meaning to what goes on in it 
proves that the world itself is rational. Rational 
thought could find no meaning in a world which was 
not itself the expression of rational thought, for 
nothing but the rational has meaning. Without 
this assumption, man's knowledge is an edifice 
without foundation. 

§ 10. — We see, then, that in every case, great as 
well as small, the material of knowledge is given us 
— we cannot make reality other than it is. But, on 
the other hand, this material only becomes intelligible 
when it is interpreted by thought. It is thought 
which makes reality known to us. In this sense 
man may be said to construct his world. Indeed, 
each one of us constructs his own world, for each 
one of us comes into contact with reality in his own 



I GENERAL NATURE OF KNOWLEDGE 25 

individual experiences, and interprets those ex- 
periences according to his own amount of knowledge. 
But no two of us have either exactly the same 
experiences or the same knowledge. Consequently, 
each one of us sees the world from a standpoint 
somewhat different from that of all others, and sees 
it through a different medium of personal knowledge. 
Yet there is common knowledge, for all knowledge is 
of the same reality, and though there are many 
minds yet there is only one kind of intelligence. 
These different individual constructions of reality in 
thought are well likened by Dr. Bosanquet to 
" drawings in perspective of the same building from 
different points of view. . . . Our separate worlds 
may be compared to such drawings : the things 
in them are identified by their relations and functions, 
so that we can understand each other, i.e. make 
identical references, though my drawing be taken 
from the east, and yours from the west." ^ It is, 
then, only by comparison of the construction of 
reality of one individual with that of another, and 
the consequent correction and enlargement of each 
by each, that we have that common knowledge which 
represents the totality of individual knowledges and 
which is the extent to which mankind has grasped 
truth. This is the universal knowledge of which the 
individual knowledge of each one of us is but an 
imperfect reflexion. 

It should be noted that this common knowledge is 
not the product of any one generation. It is the 
result of the attempts of countless generations of men 
to understand more and more of the world — attempts 
prompted from the first by practical needs, and in 
addition, in more civilized days, by the simple love of 
knowledge for its own sake. Every individual enters 
^ Essentials of Logic, p. 18. 



26 THE LOGICAL BASES OF EDUCATION ch. i 

into the heritage of the thought of the past, for he 
finds much interpretation current in the society into 
which he is born, and expressed in the language 
which he learns. Much of this knowledge he imbibes 
unconsciously, by imitation and by learning to use 
language, and much he receives by direct instruction 
from others. Thus, no individual takes up the task 
of trying to understand the world from the begin- 
ning ; he accepts much that has already been done. 
Were it not for this no growth of knowledge would 
be possible. This it is which makes the common 
knowledge of mankind an ever swelling flood, and 
enables man to read more and more fully the riddle 
of the universe. 



CHAPTER II 

POSTULATES OF KNOWLEDGE 

§ 1. — We found in the last chapter that know- The 
ledge implies both a real world and intelligence ^no^^J^d^ 
capable of understanding that world. But though 
we can distinguish these two factors of knowledge, 
they cannot be actually separated. Neither can 
exist without the other. "We cannot have thought 
about nothing ; so thought cannot exist without the 
world. On the other hand, if any reality exists out 
of all relation to human consciousness, that reality 
does not exist for man. The world exists for each 
one of us just so far as he is aware of it, and no 
further. If we extend this thought, we are led to 
see that a reality which exists for no consciousness at 
all — human or divine — is absolutely unthinkable, 
because it is devoid of meaning. We must not, 
therefore, think of man and of the rest of the 
universe as two separate orders of existence in no 
essential relation to each other. The universe is the 
whole of existence including man, and it is only 
because man is an integral part of the universe that 
he can enter into that relation to it which we call 
knowledge. 



28 THE LOGICAL BASES OF EDUCATION chap. 

§ 2. — This relation starts with the very beginning 
of experience. As Dr. Bosanquet puts it, " Experience 
may be said to begin with the certainty that ' there 
is somewhat.' " ^ The growth of knowledge is just 
the fuller and fuller understanding of that "somewhat." 
Now, this growth has been the work of many minds 
continued throughout long ages. Such co-operation in 
the increase of knowledge is only possible on the 
assumption that human intelligence always works 
fundamentally in the same way. Its products indeed 
differ, for they include all attempts to explain the 
universe, from that of the rudest savage to that of the 
most profound philosopher. But this difference is 
due to the different starting points made possible by 
the growth of knowledge itself, not to differences in 
the principles on which interpretation of experience 
proceeds. Such common principles can be found 
by analysing the process of acquiring knowledge. 
They are called the Postulates of Knowledge, because 
they are presupposed in all knowledge from the very 
beginning, and are the very life-blood of its growth. 
As knowledge grows these postulates get a wider 
and deeper meaning, but in their essential nature 
they are the same throughout. 

Of these Postulates of Knowledge four are of great 
importance. They have long been named the Principles 
of (1) Identity, (2) Contradiction, (3) Excluded 
Middle, (4) Sufficient Reason. As they are all 
operative together and each is more or less closely 
involved in each of the others, instead of examining 
them separately it will be convenient to discuss their 
combined scope at each of the three great stages of 
interpretation of the world brought out in the last 
chapter — that of sense-perception ; that of law ; that 
of system. 

1 Logic, vol. ii, p. 206. 



POSTULATES OF KNOWLEDGE 



29 



§ 3. — The distinguishing mark of the stage of sense- The 



Postulates 
at the 
Stage of 
Sense-per- 
ception— 



perception — which may perhaps be called that of un- 
educated common sense — is that the common ' things ' 
which man perceives by his senses are the ultimate 
forms of reality. Relations are regarded as indiffer- 
ent ; the things stand fast like " the everlasting hills," 
whilst relations form and scatter around them like 
the clouds, and with no more effect on their real 
nature. To this view, the world is a sum of separate 
and independent units, and the highest aim of 
knowledge is to classify and describe these correctly. 

Here the Frinciple of Identity is most prominent, identity 
It asserts that the real nature of everything is 
constant. This does not deny difference or change. 
Indeed it is only amidst diversity that identity is 
ever known. Oak-trees differ in size, shape, position, 
and in many other ways, yet they have an identi- 
cal nature, shown in a general identity of life-history. 
Time brings changes to all things more or less 
rapidly, and we learn what amount of change to 
expect, and refuse to recognize identity at all if that 
change is not there. If I see a child to-day whose 
appearance seems to me to coincide with that of a 
child I knew thirty years ago, that very resemblance 
will prevent me from believing that he is the same 
person. Identity, then, is always found amidst 
diversity. 

The Frinci2?le of Contradiction is essential to give 
a full and precise meaning to that of Identity. It 
asserts that the same nature cannot have contra- 
dictory qualities, or, in other words, that a statement 
and its denial cannot both be true. Of course, the 
statement and its denial must both refer to the same 
piece of reality at the same time. Yesterday I could 
truly say, " I have a headache " ; to-day with equal 
truth I can deny the headache. But these two 



Contradic- 
tion. 



30 THE LOGICAL BASES OF EDUCATION chap. 

statements are not contradictory, or in any way 
incompatible, for though both refer to "I," yet the 
" I " in the one case is the " I of yesterday " and in 
the other case the " I of to-day." Indeed the prin- 
ciple of Identity may be expressed by saying that 
" what is once true is always true " — for if the state- 
ment refers to anything which changes with time, it 
does so within definite time limitations. The time 
limits may be very narrow, as in the case just quoted, 
or they may be of considerable extent. When a 
statement concerns the essential nature of a thing, 
its time limits are coextensive with the existence of 
that thing. Thus the statement that " oaks spring 
from acorns " must be held as true for all oaks that 
ever have been or ever will be in the world. Here 
we see how the principles of Identity and Contra- 
diction complement each other : that of Identity says : 
oaks are always produced from acorns ; that of Con- 
tradiction denies that they can ever be produced in 
any other way, or that any other growth can spring 
from acorns. 
Excluded The Prificijole of Excluded Middle afiirms that 
either a statement or its denial must be true, and 
thus completes the Principle of Contradiction, which 
says that one of them must be false. An important 
bearing of this is that when we prove a statement 
to be false we necessarily prove that its denial is 
true. Of course, this principle must be understood 
with the same strictness as those we have already 
discussed. It does not imply that we are always 
sure which of two contradictory statements is really 
true. In every case of doubt we are unable to de- 
cide this because, in some way, we have not sufficient 
knowledge of the matter in hand. We may be un- 
able by lifting them to determine which of two nearly 
equal weights is the heavier, yet one of them is 



Middle. 



Reason. 



II POSTULATES OF KNOWLEDGE 31 

the heavier, and a pair of scales may decide the 
question. The doubt is not in the things themselves, 
but in our interpretation of the effect they produce 
upon us. 

The Principle of Sufficient Reason affirms that Sufficient 
everything is capable of explanation. At the stage 
of knowledge we are now considering such explanation 
is always imperfect, and very often more or less 
fanciful. As we saw in the last chapter, savages — 
who are the most thoroughgoing representatives of 
this stage of thought — do seek explanation, but they 
seek it mainly in the activity of supposed super- 
natural beings. Indeed, as soon as men seriously 
seek an explanation for the events they see around 
them, they begin to pass into the next stage of 
thought. 

§ 4. — The characteristic of the second — or The 
scientific — stage of interpretation is the attempt to ft^the s 
explain everything in the world by its relations to of Law. 
other things. As has been already pointed out, 
modern physical science pushes this explanation of 
the things of sense-perception so far that it nearly 
explains them away altogether. It finds the 
ultimate reality in the relations to each other of 
simple and unchangeable atoms, and teaches that 
constancy in the nature of ' things ' is due to con- 
stancy in the relations between their constituent 
atoms. The principles of Identity, Contradiction^ 
and Excluded Middle are, therefore, given a wider 
application. They apply now primarily to the 
relations of atoms, and only secondarily to the 
' things ' constituted by such relations. 

Moreover, modern science insists on the truth that 
these ' things ' are in relations to each other, and 
change with every alteration in such relations. The 
actual phenomena of the universe can, then, only be 



82 THE LOGICAL BASES OF EDUCATION char 

understood when relations of thing to thing are 
investigated. This emphasizes the Frinciple of 
Sufficient Reason, but also involves the other prin- 
ciples. For as similarity in the nature of things is 
explained by the assumption of similarity in relations 
between the constituent atoms, so similarity of 
change is explained by assuming similarity in the 
relations of the things involved. We speak here of 
' similarity ' rather than of identity, because, as has 
been already pointed out, identity is never found 
except amidst diversity, and ' similarity ' expresses 
this very combination, and is, therefore, the most 
appropriate term to apply to the actual events which 
take place in the universe. In all similar phenomena 
there is an element of identity to which the simi- 
larity is due, and on the basis of which alone we can 
infer from one to the other. But this element of 
identity is by no means always on the surface ; in 
many cases, indeed, we have to assume its existence 
without being able to specify exactly either its nature 
or its extent. As Mill reminds us : " The course of 
nature, in truth, is not only uniform, it is also 
infinitely various. Some phenomena are always seen 
to recur in the very same combinations in which we 
met with them at first ; others seem altogether 
capricious ; while some, which we had been accus- 
tomed to regard as bound down exclusively to a 
particular set of combinations, we unexpectedly find 
detached from some of the elements with which we 
had hitherto found them conjoined, and united to 
others of quite a contrary description." ^ 

To first experience, then, the world is chaotic, 

and, as we have seen, the savage so regards it. This 

is because he applies the Principle of Identity only to 

things, in the independent nature of which he seeks 

^ Logic, vol. i, p. 359. 



II POSTULATES OF KNOWLEDGE 33 

all explanation. " Man after man dies in the same 
way, but it never occurs to the savage that there is 
one constant and explicable cause to account for all 
cases. Instead of that, he regards each successive 
death as an event wholly by itself — apparently un- 
expected — and only to be explained by some super- 
natural agency." ^ It is only when the importance of 
relations is recognized and the postulates of know- 
ledge applied to them, that the conception that 
underneath all the apparent confusion of phenomena 
there is an always present and essential uniformity 
begins to govern man's mode of interpreting his ex- 
periences. Then science begins, for man recognizes 
that upon him " is imposed the task of everywhere 
seeking out in the natural phenomena those elements 
that are the same, and that amid all multiplicity are 
ever present." ^ When such elements are found, the 
work of science is done. " When once we have 
reached the point where we are everywhere able to 
detect the same few simple elements combining in 
the ordinary manner, then they appear to us as 
things that are familiar ; we are no longer surprised, 
there is nothing new or strange to us in the pheno- 
mena, we feel at home with them, they no longer 
perplex us, they are explained.^^ ^ 

The explanation given by science, then, consists in Causation. 
determining the conditions under which any change 
or event takes place. And the whole of these con 
ditions together are styled the Efficient Cause — or 
simply the cause — of the phenomenon in question. 
The Principle of Causation is, then, one aspect of 
that of Sufficient Reason. Its most general axiom 
is : (1) "Every event must have a cause." Then, in 
combination with the principle of Identity and its 

^ Lionel Decle, Three Years in Savage Africa, p. 512 

- Mach, Science of Mechanics, p. 5. ^ Ibid., pp. 5 — 6, 



34 



THE LOGICAL BASES OF EDUCATION chap. 



complementary principles, it assumes uniformity in 
causation in the axioms — (2) " The same cause always 
produces the same effect ; " (3) " The same effect is 
always due to the same cause ; " (4) " Cause and 
effect are equal in amount of energy." 

As we have seen, the first of these four axioms is 
implied in all attempts to explain the world ; even 
the rudest savage assumes it. But the other three 
axioms are only operative when explanation is sought 
in relations. Then, as man's early seekings after 
knowledge are always motived by practical needs, 
the uniformity of causation appeals to him first in 
the light of the second axiom. He is interested more 
in what will result from certain conditions than in 
the inverse problem of what conditions have produced 
a given result. Hence, he studies causation mainly 
from the point of view of the cause. In other words, 
he analyses more or less carefully the conditions that 
will give a certain desired result, and he assumes 
that if the result comes in one case it will come in 
all, provided that he secures the same conditions. 
He applies the principle of Causation forwards. 

But the result obtained is often a very general one, 
and man's practical needs do not usually prompt him 
to analyse it carefully. Hence it often appears to 
superficial observation that the third axiom is not 
true, and that the same effect may be produced by 
different causes on different occasions. If this were 
so, the principle of Causation would be one-sided, for 
the principle of Identity would be only half applic- 
able to it. And, indeed, this was the common 
opinion till quite recently. Even the savage recog- 
nizes some uniformity of causation in cases in which 
his own activity in carrying out his own purposes 
plays an important part. He desires to kill his 
enemies or the animals he requires for food, and he 



II POSTULATES OF KNOWLEDGE 35 

knows he can do this in a variety of ways. When 
he sees death which has not resulted from visible 
violence, he assumes that a similar destructive activity 
is exercised by malignant spirits. Death, then, to 
his mind, obviously results from a variety of causes. 
Nor is the savage alone in this rough and ready way 
of interpreting events. Even so great a logician as 
Mill says : " It is not true that only one effect must be 
connected with only one cause, or assemblage of con- 
ditions . . . many causes may produce death." ^ But 
in speaking of "death " Mill shows that he has not 
applied the same searching analysis to the effect 
which he tells us is necessary to discover the cause. 
Every coroner's inquest is an attempt to perform 
such an analysis, and of necessity proceeds on the 
assumption that exactly the same kind of effect can 
have only one cause. There is no such thing as 
death in general ; every death is one particular kind 
of death, and in speaking of ' death ' as the effect of 
a bullet through the head or of swallowing arsenic, 
we are either using the word very loosely or we 
are picking out from the total effect the one factor 
which is of the greatest personal interest. A hole in the 
head is just as much part of the effect of the bullet 
in the first case as is the death, and similarly a 
particular condition of the organs of the body 
results from taking arsenic just as surely as does 
death. 

No doubt, at first sight it seems certain that the 
same effect is due now to one cause, now to another. 
" Thus friction, combustion, the liquefaction of a 
vapour, freezing, pressure, all produce heat. What 
could be more apparently disparate than these agen- 
cies 1 Yet all of them alike involve the liberation 
of molecular motion in accordance with mechanical 
^ Logic, vol. i, p. 505. 

D 2 



36 



THE LOGICAL BASES OF EDUCATION chap. 



laws common to all the cases." ^ This example 
admirably brings out the difference between the popu- 
lar and the scientific views of causation. The 
former confines itself to the sphere of sense-percep- 
tion, and finds causation in the influence of one 
visible and tangible body upon another ; the latter 
seeks it in an analysis of the process which brings to 
light a persistent and identical nature changing in 
determinate ways under definite conditions. In all 
cases, such an analysis is a task of difficulty ; in many, 
it has not yet been accomplished. But the belief 
that, when such an analysis is found possible, it will 
always reveal an underlying identity, even amidst 
the greatest apparent diversity, is involved in the 
acceptance of the axiom that causation is uniform. 

As the third axiom was recognized later than the 
second, so the full scope of the fourth can only be 
seen when the third is accepted. It is a yet further 
application of the principle of Identity to that of 
Causation, and when stated in its most general form 
it becomes the doctrine of the conservation of energy 
— that the amount of energy in the world is not 
subject to either decrease or increase, but only to 
change in mode of expression. This is one of the 
latest conceptions of modern physical science, but we 
see in it only the further application of the same 
principles of interpretation which have been operative 
from the first in the development of knowledge. 

A consideration of these axioms of causation makes 
it evident that, in another respect, the common 
way of regarding causation is indefinite. We con- 
stantly look upon the cause as necessarily preceding 
the effect in time. Indeed, not infrequently mere 
succession in time is mistaken for a true causal con- 
nexion, as when the appearance of comets is held to 
1 Hobhouse, The Theory of Knoivledge, p. 366. 



II POSTULATES OF KNOWLEDGE 37 

be the cause of a war or other calamity, which may 
follow shortly after. It can easily be shown, however, 
that the cause does not always precede the effect. 
A blot is the effect of letting a drop of ink fall on 
paper, but the blot does not follow the contact of ink 
with paper ; its appearance is simultaneous with that 
contact. So the height of the mercury in a barometer 
is the effect of the pressure of the atmosphere, but it 
is simultaneous with that pressure. In other cases, 
the effect seems subsequent to the cause. A cricket 
ball is struck by a bat, and the motion of the ball is 
subsequent to the stroke which was its cause. But 
here again we want a deeper analysis of the process. 
The impulse given by the bat is communicated to the 
ball in the moment of impact, and not subsequently 
to that moment. Thus it is the accumulated effect 
which is subsequent to the original stroke, and 
further analysis shows that we have a continuous 
transition of events each of which is at once cause and 
effect. 

Whether we say, then, that effect follows cause 
or is simultaneous with it depends upon how we 
are using the terms. This is admirably put by 
Whewell : " The instantaneous effect or change is 
simultaneous with the instantaneous force or cause 
by which it is produced. But if we consider a series 
of such instantaneous forces as a single aggregate 
cause, and the final condition as a permanent effect 
of this cause, the effect is subsequent to the cause. 
In this case, the cause is immediately succeeded by 
the effect. The cause acts in time : the effect goes 
on in time. The times occupied by the cause and by 
the effect succeed each other, the one ending at the 
point of time at which the other begins." ^ 

In brief, we must remember the continuity of 
1 History of Scientific Ideas, vol. 1, pp. 197 — 198. 



38 THE LOGICAL BASES OF EDUCATION chap. 

change in the world, and the artificial character of 
what we single out as ' events.' As Mr. Hobhouse 
says : " No event ever begins or ends ; but a process 
goes on which passes gradually from one phase into 
another. We ticket prominent or clearly distinct 
phases with separate names, and speak of them as 
different events ; but we must remember that, though 
in one sense they are different, there is yet no 
barrier."^ 'Cause' and 'Effect,' in the common 
use of the terms, are but separate names for artificially 
limited earlier and later phases in one continuous 
process. 

Causality is, then, a principle on which the human 
mind acts from the first. It is not gathered from sense- 
experience, for it is involved in all interpretation of 
such experience. " What causes produce what effects ; 
what is the cause of any particular event ; what will 
be the effect of any peculiar process ; these are 
points on which experience may enlighten us. . . . 
But that every event has some cause, experience 
cannot prove any more than she can disprove." ^ 
Nor can experience demonstrate that one cause is 
universally connected with one effect. But this is 
assumed in the statement of every scientific 'law,' 
for such laws assert that a causal relation which has 
been observed in a limited number of cases holds 
true throughout the universe, and this is, obviously, 
not a matter which can be either proved or disproved 
by observation. The establishment of such laws is 
the ideal of knowledge at this stage. 
The § 5. — We saw, however, in the last chapter, that 

at°tiS stage explanation by bringing a particular case under a 
of System, general law cannot be ultimate, and that we are 
driven by the necessities of thought to regard the 

1 The Theory of Knowledge, p. 277. 

2 Whewell, op. ciL, p. 174. 



n POSTULATES OF KNOWLEDGE 39 

universe as one self-determined system. With this 
conception we have obviously a very considerable 
extension of the principles of interpretation beyond 
their application in the scientific stage. The 
universe itself, as well as its constituent parts, is 
now regarded as embodying those principles. It is 
thought under Identity as a continuous unity retain- 
ing its essential nature amidst all the infinite number 
of varied manifestations of that nature. Under 
Contradiction it is thought as essentially consistent ; 
as containing no contradictions. This is why we find 
contradiction always a proof of error, for this principle 
compels us to recognize that error cannot ultimately 
be made consistent. Under Excluded Middle we 
think of it as a system of mutually-determined parts. 
Lastly, under Sufficient Reason we regard it as 
furnishing in the relations of part to part the first 
stage of explanation, and in the relation of parts to 
the whole an ultimate explanation. 

In discussing the scientific method of interpretation Final 
we saw that it is mechanical, that is, it explains one ^^^^^®^- 
phenomenon by its relations to others according to 
mechanical laws. We have also seen that this 
explanation is not final. The conception of eJ0&cient 
cause which dominates scientific interpretation is 
supplemented in the philosophical stage by the con- 
ception of purpose. This is iijherent in the con- 
ception of system. To revert to the illustration of 
the watch. The efficient cause of its marking the 
time is the relation of part to part. But that does 
not explain why the watch exists. This is found 
in the human purpose which it serves. The watch 
is planned and made by man just for that very object, 
and without it the watch would not exist. This 
conception of purpose — or Final Cause, as it is 
frequently called — is moulding more and more man's 



40 THE LOGICAL BASES OF EDUCATION chap. 

interpretation of the world. Of course, the purpose 
is not always relative to man. It is so in the case 
of things like the watch, which he invents and makes 
to serve his own ends. But we have got beyond the 
stage of thought in which sun, moon, and stars were 
regarded as existing solely for the purpose of giving 
man light, and in which efforts were made to find a 
reason for the existence of everything by showing 
that it is of some use to man. Such an attempt was 
common enough even in the eighteenth century, and 
perhaps reached its highest point of absurdity when 
the existence of noisome domestic insects was 
accounted for on the ground that such pests induced 
personal cleanliness. 

We now regard each form of existence as having 
its own purpose. Of course such purpose can only 
be known by beings endowed with minds. Man can 
aim at attaining a certain form of character, and 
even the lower animals are conscious of wants which 
they strive to satisfy. But the modern doctrine of 
evolution finds progression in the vegetable as well 
as in the animal world, and we may quite intelligibly 
speak of the purpose of the existence of oak-trees as 
the gradual attainment of the perfection of oak-tree 
life. Even in the inorganic world we must 
think of all change as the gradual attainment of 
some end, though we must not try to find that end 
in reference to the needs of men. In so far as any 
thing freely manifests its own nature it may be said 
to fulfil its purpose. Thus we think all change as 
having an object, though that object is often hidden 
from us. As Dr. Harris puts it : "In the view of 
evolution there is a goal towards which relatively 
lower orders are progressing, and the facts, forces, 
and laws are seen as parts of a great world-process 
which explains all. At this point science rises into 



11 POSTULATES OF KNOWLEDGE 41 

philosophy. ... When science comes to study all 
objects in view of the principle of evolution, it has 
transcended the stage of mind whose highest object 
is to discover classes ; likewise the stage that makes 
law an ultimate. Besides efficient cause, which 
makes or produces some new state or condition, there 
is ' final cause ' or purpose — design or ' end and 
aim.' " ^ 

' Psychologic Foundations of Education, pp. 19 — 20. 



CHAPTER III 



KNOWLEDGE AND LANGUAGE 



Ideas and 
Knowledge. 



Ideas and 
Reality. 



§ 1. — We have seen that all knowledge consists in 
correctly interpreting or giving a meaning to ex- 
perience, and that such interpretation means the 
harmonizing this experience with others. Or we 
may put it in another way, and say that to give 
meaning to any piece of reality is to think it in its 
proper place in an appropriate system. But systems 
of reality exist in consciousness as mental construc- 
tions, or ideas. Hence, to give meaning is to think 
an experience under an idea already existing in con- 
sciousness. We may say, then, that experience as 
interpreted is made up of ideas, and that knowledge 
consists of all those ideas which are proved true. 

§ 2. — But reality to each of us is only our 
experience as thus interpreted. Therefore, by 
' ideas ' is meant the way in which the mind grasps 
reality. Every known piece of reality exists in 
consciousness as an idea. It is not merely represented 
in consciousness, as if the world of reality were 
separate and distinct from the world of knowledge. 
We must not, therefore, think that things in the 
external world impress copies of themselves upon our 



CH. Ill KNOWLEDGE AND LANGUAGE 43 

minds, as a seal stamps impressions on wax, or as 
the image of an object is impressed on a photographic 
plate. It is true the retina of the eye does act 
very similarly to a photographic plate, but the eye is 
not the mind, and the retinal image is not itself in 
consciousness. 

§ 3. — It is true also that we talk of the " eye of ideas and 
the mind," and that most people can call up more or ^^^s^^- 
less vivid and distinct mental images of absent 
objects. Images, however, are not ideas, but only 
symbols of ideas. Just as the shape and colour of an 
orange are symbols of all else that ' orange ' means 
to us when the orange is actually present to per- 
ception, so the visual image of an orange acts as a 
sign in exactly the same way. The idea is the 
meaning which the mind finds for the present ex- 
perience by referring it to other experiences, and any 
mental image that may come into the mind is only 
an example or illustration of that meaning. 

In many cases, indeed, such images do not corres- 
pond to the idea, and when present tend to obscure 
meaning and hinder understanding. " We can image 
some object that is acted upon by force — we can 
image it before it is acted upon and after it is acted 
upon. That is to say, we can image the results of 
the force, but not the force itself. We can think of 
force, but not image it." ^ To "have an idea" of 
anything is, then, to know its nature and meaning ; 
in other words, to think it, not to look at it either in 
reality or as represented in a mental image. 

Doubtless, real thought is difficult, and many Thought 
persons are satisfied to substitute for it panoramas imagma- 
of mental pictures. This tendency is promoted by *^°^- 
" what we may call the Photographic writing which 
alone obtains at present. For a long while back, writers 

' Harris, Psychologic Foundations of Education, p. 40. 



44 THE LOGICAL BASES OF EDUCATION chap. 

have desired to write only to our eyes, not to our 
thoughts. History now is as a picture-gallery, or 
as a puppet-show ; men with particular legs and par- 
ticular noses, street-processions, battle-scenes, — these 
— images — all images ! — mow and mop and grin on us 
from every canvas now. We are never asked to 
think — only to look — as into a peep-show, where, on 
the right, we see that, and on the left this ! " ^ 

It is true, as Dr. Stirling himself reminds us, 
that images "are always the beginning, and con- 
stitute the express conditions, of thought." ^ Whilst 
an individual is in the first stage of thought — that 
of sense-perception — he will not have separated his 
meanings from his images and his percepts. But 
unless we pass beyond this stage to that of the 
abstract idea, or meaning, " we never attain to 
mastery over ourselves, but float about a helpless 
prey to our own pictures." ^ This is so because all 
such pictures are of individual and particular things, 
and every particular exhibits qualities and relations 
of its own, which are not part of the meaning, and 
which obscure that meaning. For example, all 
who have worked problems in geometry know how 
easy it is to be misled by some accidental feature of 
the particular diagram we draw, or picture in our 
minds, to aid us in the solution. We desire, it may 
be, to establish some relation of triangles in general, 
and the particular triangle we draw has perhaps 
two of its angles equal, and we are apt to treat this 
accidental relation as essential, and base our proo* 
upon it. In contrast to the particular image, mean^ 
ing is always universal ; that is, it is common to all 
pieces of experience which we think under the '^ame 
idea. 

^ Stirling, The Secret of Hegel, p. xlii. 
^ Ibid., p. xliii. ^ Ihid. 



Ill KNOWLEDGE AND LANGUAGE 45 

§ 4. — If we now ask how knowledge, or a system Deveio; 
of meanings, develops in an individual mind we are idtas° 
at once met by a theory once very commonly ac- 
cepted but now proved to be thoroughly false. 
According to this theory, the mind begins with ideas 
of individual things, then, by comparison, classes 
them together, and so goes on to construct its world 
in a manner very similar to that in which a brick- 
layer builds a wall. Nothing could be farther 
from the truth. Modern psychology has thoroughly 
established that the mind begins with a vague 
apprehension of its experience as a whole, and then 
little by little divides this up, as this or that piece of 
experience secures its interest and special attention. 
As Dr. Bosanquet suggests, the process may be illus- 
trated by " the discernment of features in a distant 
landscape which prolonged attention even without 
optical assistance has the power to effect." ^ The 
process starts from the whole, not from the elements. 
Ideas of classes are formed out of wider and vaguer 
ideas as striking differences attract the attention. 
The first idea is of a vague " something," and from 
this by continual division more and more definite 
ideas of different forms of reality are evolved. But 
at every stage the ideas reached are used to interpret 
fresh experiences which are gathered under them. 
Thus in the process of the development of know- 
ledge, analysis — or splitting up, and synthesis — or 
binding together, go hand in hand. 

I § 5. — This process would be impossible without a ideas and 
system of signs by which, on the one hand, attention 
cbixxrbe concentrated on one element in the complex 
who]^^<)f which experience at every moment consists, 
and on the other hand, the ideas, when once reached, 
can be represented symbolically in consciousness. 
^ Logic, vol. i, p. 32. 



Language. 



46 THE LOGICAL BASES OF EDUCATION chap. 

Any such system of signs is a language. Thus, 
even in the individual mind, knowledge could not 
develop without a language of some kind. 
Language § 6. — Even easier is it to see the necessity of 

n?ra,tion?f^ language when we consider the growth of know- 
Knowledge, ledge, not in an individual mind, but in the race. 
We have seen that this growth depends on com- 
munication of knowledge between men. But such 
communication implies a common language, or system 
of signs whose reference to reality is generally 
accepted and understood. This, in turn, implies that 
the signs are also instruments of individual thought : 
language as a means of communication rests upon 
language as a means of individual thought. 
Verbal § 7. — Of all systems of signs for thinking and 

anguage. communicating thought, words are by far the most 
convenient, because, owing to their conventional and 
artificial character, they can sustain a much more 
general and abstract meaning than can any other 
thought-symbols. Thus, as knowledge advances, 
language becomes more and more exclusively verbal. 
Savages convey much of their meaning by descriptive 
gestures, and some of the least developed in intelligence 
have so poor a language of words that they cannot 
understand each other in the dark, because the gestures 
which fill out their speech cannot be seen. But 
gestures have very similar disadvantages to mental 
pictures as symbols for thought. Like visual images 
they can only represent the outward and visible 
qualities, and these are frequently far from being 
the most important. Gestures are also frequently 
doubtful in their reference ; a flapping of the arms, 
for instance, may represent either a bird, or the act 
of flying. With a language wholly or mainly of 
gestures, then, knowledge could advance but a little 
way even on the stage of sense-perception. Hence, 



Ill KNOWLEDGE AND LANGUAGE 47 

a system of conventional signs, capable of express- 
ing meaning v/ith any required degree of definiteness, 
is essential to really developed thought. Speech 
fulfils this requirement, and has the additional ad- 
vantages that it is easily produced, can be used as a 
means of communication in the dark as well as in 
the light, and between persons at some distance from 
each other, an advantage which the modern applica- 
tions of electricity have enormously increased. 

Writing is, of course, only verbal language in writing. 
another form, but it plays a part in the development 
of knowledge which nothing else could have played, 
in that it extends the communication of knowledge 
to an indefinite extent, and renders possible contact 
of any one individual mind with many other minds 
both in the present and in the past. It is mainly by 
means of written language that the knowledge of the 
individual on the one hand contributes to the 
knowledge of the race, and on the other hand is 
checked and corrected by it. And such correction 
is necessary. For, as experience is interpreted by 
experience, and as the experiences of every individual 
differ from those of every other individual, it 
follows that various interpretations of the same 
piece of reality may be given by different 
persons. Were the interpretations of each person 
wholly dependent on his own narrow range of ex- 
perience, this would certainly be the case to an 
appalling extent, and, of course only one at most of 
a set of incompatible interpretations can be true. 
Even now we find plenty of such variations ; every 
" difference of opinion " is a case in point. But 
when we can test our ideas by the experiences of 
innumerable other people, we are much more likely to 
reach the truth at last. Such testing goes on through- 
out life by means of both written and spoken language. 



48 THE LOGICAL BASES OF EDUCATION chap. 

Language § 8. — When a child learns his mother tongue, the 
Learning, words he acquires are from the first signs of ideas, in 
that they are referred to certain pieces of reality. 
His ideas are doubtless extremely imperfect at first, 
but the fact that the reference to reality is the same 
to him and to others, renders instruction possible. 
He may, for example, find himself ignorant of nearly 
everything concerning a certain flower which he has 
seen and the name of which he has learnt. But he 
can seek instruction- from another person whose idea 
of that flower is full and accurate, and therefore very 
different from his own. And he can do this because, 
though the ideas are different, yet their reference to 
reality is the same. And that identity of reference is 
marked by the name, so that to utter the name 
indicates what the child wants fuller information 
about as clearly as showing the actual flower would 
do. But such instruction is effectual only so far as 
the teacher uses words which have a clear meaning 
to the child, that is, which call up in his mind 
definite ideas. It is by combining these ideas that 
he is led to form a fuller and more accurate idea of 
the flower than he had at first. . 

The same process makes it possible to lead the 
child to form ideas of parts of reality he has never 
experienced. " We wish to describe quicksilver to 
a child. We say that it is something like this pew- 
ter in its brightness and the way it reflects the light ; 
it is even heavier than this lead ; it is liquid like 
water, so that I could pour it from one vessel to 
another. And we might further qualify each of 
these statements so as to render them more exact. 
Now/ we may assume that all the w^ords in which 
the quicksilver is described are significant to the 
child ; if they are not significant the description so 
far fails. At the end. if he have good powers of 



Ill KNOWLEDGE AND LANGUAGE 49 

synthesis, he may combine these particular properties 
thus signified into the new idea we wish him to form. 
The word ' quicksilver ' then becomes significant to 
him."i 

It is in this way that we all gain knowledge in- 
directly, through the verbal testimony of others to 
parts of reality which we have not ourselves experi- 
enced. It is evident, however, that such indirect 
knowledge must rest ultimately upon that direct 
knowledge of reality which springs from our own 
experiences, and which alone can give meaning to 
the language by which indirect knowledge is com- 
municated. It is this which makes it all important 
that in early life, not only should the ideas which a 
child gains through careful examination and analysis 
of direct experience be as numerous, full, and exact as 
possible, but that they should be correctly associated 
with language. This is the foundation of that 
thorough command over language without which all 
good mental work is impossible, and which it is, 
therefore, one of the chief duties of the educator to 
develop in his pupils. 

§ 9. — Communication of thought and knowledge. Spoken and 
then, depends on the existence of corresponding ideas Language. 
in different minds. By " corresponding ideas " is 
meant ideas which refer to the same reality and give 
substantially the same meaning to it. The ideas of 
different people will hardly coincide more closely than 
this, owing to the differences of experience from 
which those ideas have sprung.^ Now it is evident 
that if the ideas of the hearer or reader differ 
materially from those of the speaker or writer, grave 
misunderstanding may arise. This may be avoided 
in oral communication by questioning, on the one side 

^ Lloyd Morgan, Psychology for Teachers, p. 178. 
2 Of. p. 25. 



50 THE LOGICAL BASES OF EDUCATION chap. 

or the other, on any point whose interpretation seems 
doubtful. But writer and reader are much more at 
each other's mercy. On the one hand, the reader 
may bring a number of false preconceived ideas to 
the interpretation of his author, or he may read 
carelessly and hurriedly. In both cases wrong 
meanings are attributed to the writer and the 
corrective of oral intercourse is absent. As Plato 
long ago said, "Speeches , . . when they have been 
once written down are tumbled about anywhere 
among those who may or may not understand them, 
and know not to whom they should reply, to whom 
not : and, if they are maltreated or abused, they 
have no parent to protect them ; and they cannot 
protect or defend themselves." ^ On the other hand, 
the writer may have expressed himself obscurely, and 
the reader be unable to grasp his meaning, not from 
carelessness or poverty of ideas, but from being 
doubtful exactly what it is the author wishes to say. 
A question would lead to the solution of his difficulty, 
but if you question a printed page it " always gives 
one unvarying answer."^ On the other side, it may 
be truly urged that the printed page has an advan 
tage over the oral teacher in that it is always ready 
to be questioned, and bears the dulness or perversity 
of the scholar with a great deal more patience than 
the living teacher is apt to do. 
Meaning § 10. — The liability to misunderstanding is enor- 
mously increased when speech is ambiguous. Am- 
biguity is possible because every word has its mean- 
ing partly determined by its context. As was 
pointed out in speaking of the development of ideas, 
we do not begin with ideas of separate things and 
weld them together, but we begin with a vague idea 
of a whole which we have to analyse. Now, 
1 Phaedrus (Jowett's Translation), p. 275. ^ Ibid. ^ 



and 
Context. 



Ill KNOWLEDGE AND LANGUAGE 51 

language symbolizes ideas. We must look for the 
beginnings of language, then, in actual speech, not in 
isolated words. Indeed, in early stages of language 
there is no division into words, either in speech or in 
writing. "It is always very late in the day before 
the seminal principles of speech are detected and 
explained. Indeed, the language which owed to 
them both birth and growth may have ceased to be 
a living tongue before these, the regulative elements 
of its formation, come to light and are embodied in 
written grammar. That most elementary species of 
instruction which we familiarly term the A, B, C, 
had no express or articulate existence in the minds 
or on the lips of men, until thousands of years 
after the invention and employment of language ; 
yet these, the vital constituents of all speech, 
were there from the beginning."^ Knowledge of 
language, like knowledge of every other part of 
reality, works at first from the whole towards the 
elements. 

All portions of speech, then, depend for their full 
meaning upon the context in which they exist. For 
example, my idea of the relation of logic to education 
is expressed in this book as a whole, though even 
that total idea, as we may call it, owes its character 
to its relation to the rest of my mental life. How- 
ever, taking that as a sufficiently self-contained 
whole, it is evident that the full meaning of each 
chapter involves the relation of the idea expressed 
by that chapter to the whole idea developed in the 
book. Similarly, the idea set forth in each para- 
graph depends for its full meaning upon its relation 
to the rest of the chapter ; the idea expressed by 
each sentence is relative to the paragraph of which it 
forms a part. With the sentence we have reached 
^ Terrier, Institutes oj Metaphysic, p. 15. 

E 2 



52 THE LOGICAL BASES OF EDUCATION chap. 



the unit of thought. It is true that the sentence is 
composed of words, and if we speak or write it, 
the words have to appear separately. But in 
thought the sentence exists as one idea. We may- 
write or say "The ground is covered with snow," 
but that expresses a single and undivided fact of 
experience. We are so accustomed to the gram- 
matical treatment of language as composed of words, 
and to seeing single words defined in a dictionary, 
that we are apt to overlook the truth that isolated 
words are, as Mr. Hobhouse well says, mere " dead 
fragments of language." ^ If we hear an isolated 
word, e.g., "Fire," we either regard it as an 
abbreviated sentence — that is, as intended to convey 
some information — or we are thrown into a state of 
mental perplexity as to what idea the speaker* wishes 
to convey. It is related that a famous head-master 
once dumbfounded the whole of his sixth form by 
commencing a lesson with a question propounded in 
the single word ' Abraham V Such considerations 
make it clear that each word depends for much of its 
meaning on its context. For example, we speak of a 
bright day, or a bright boy, but the force of " bright " 
is by no means identical in the two cases. The word, 
then, is relative in meaning to the sentence, and the 
sentence to the context in which it occurs. Isolated 
sentences, like isolated words, do not occur in actual 
thought, though they have to be used for illustrative 
purposes in text-books on logic and grammar. But 
if we take such a sentence as " The fire is out " we 
see at once that its meaning is very different when it 
is spoken in reference to my study or to a row of 
warehouses. The same is true throughout : a 
sentence — despite the assertions of many grammar 
books — does not express a comjDlete thought, but only 
^ The Theory of Knowledge, p. 164. 



Ill KNOWLEDGE AND LANGUAGE 53 

the smallest separable element in the ever-moving 
and living thought process. 

The exact meaning, then, in which sentences or 
words are used is determined by the general topic of 
thought. That is why no confusion is caused by the 
fact that some verbal signs have two or more distinct 
meanings, as, for instance, a ' page ' may be a boy or a 
piece of paper. No doubt ever arises in the use of 
such signs, though their existence makes punning 
possible. In fact, as they stand for distinct ideas, 
they are really distinct words, though they happen to 
have the same form. When we hear a lecture or 
read a book each portion receives much of its mean- 
ing from all that has gone before. Indeed, it is often 
impossible to understand the latter part unless the 
earlier has been grasped. Frequently, too, the 
meaning is shaded by our anticipation of what 
is coming. We see, then, that we can only fully 
appreciate the meaning of words when we think of 
them as elements in sentences which are themselves 
elements in an organic whole or system of thought. 

Every word, then, as used in the expression of actual Specific and 
thought, has a specific meaning which varies according Meardngs of 
to the context in which it occurs, that is, according to ^^rds. 
the system of thought it helps to express. Still, these 
specific meanings have much in common. There is to 
every word a general meaning which is always present 
and forms the bond of connexion between the many 
occasional meanings, and this general meaning when 
explicitly stated we call the definition of the word. 

The nature of definition will be considered in a 
later chapter ; ^ it is sufficient to point out here that 
even when we have clearly grasped the true general 
meaning of a word, we never use the word in that 
general sense alone. Just as there is no such thing 
^ See Chapter xvi. 



54 THE LOGICAL BASES OF EDUCATION chap. 

as a child in general corresponding to the general idea 
of child, but every embodiment of that general idea 
is a very individual little boy or girl, so every time 
we use the word ' child ' in a real process of thought 
the general idea which corresponds to that word is 
modified by the nature of the particular thought. Our 
knowledge of general meaning, then, does not alter 
the fact that in actual use every word is modified in 
meaning by its context ; the general meaning is a 
kind of nucleus round which the occasional meanings 
wax and wane, but some such occasional meaning is 
always present. 

Even in scientific terms, where the general mean- 
ing is not only most definite but most prominent, 
there is yet a slight occasional meaning. ' Oxygen ' 
has a quite fixed meaning, but when we think of 
oxygen we always do so in some particular connexion 
— for example, as combining with hydrogen to form 
water — and so the whole thought determines the exact 
force of the word ' oxygen ' in the actual sentence. 
Scientific terms, however, are much less flexible than 
the words of ordinary speech. Fortunately they are 
generally so long and so ugly that there is little 
danger of their ever becoming constituents of ordinary 
discourse. We say fortunately, because it would be 
a great loss were language to decrease in flexibility. 
The tendency, however, is naturally all the other way. 
And it should be noted that this flexibility marks the 
meanings of all words. Even such a little word as 
in differs in meaning in such sentences as "I am in 
trouble " and " I am in London ; " and the equally 
simple word and can be used conjunctively or adver- 
satively. Indeed, every word whatever is always a 
factor in expressing a certain idea and has its 
meaning modified according to the idea to be 
expressed. 



KNOWLEDGE AND LANGUAGE 



55 



§ 11. — There are enormous advantages in this flexi- Ambigui- 
bility of meaning, for it makes it possible to express Language, 
an innumerable number of shades of meaning with a 
comparatively limited vocabulary. The English 
peasant expresses all his thoughts with a few hundred 
words, and it is computed that even Shakespeare 
made use of only some twenty thousand words ; yet 
what a wealth of thought and feeling he uttered with 
them ! But, like all other good things, the flexibility 
of meaning has also a grave disadvantage — the con- 
sequent liability of language to become ambiguous to 
which reference has already been made. Now 
ambiguity is at bottom indefiniteness in the reference 
to reality. Such indefiniteness may be due to un- 
certainty as to the sense in which a particular word 
is used or to faulty construction of a sentence. 

In the case of individual words the doubt may 
affect the general meaning. For with the course of 
time even general meanings may change, often by 
some one class of occasional meanings displacing all 
others, or by new occasional meanings being adopted. 
Such changes are continually going on in every living 
language, though the existence of written and printed 
literature enormously retards the process. At any 
one period it may be doubtful how far the change 
has gone. Such a question cannot be determined by 
etymology or by appeal to former usage. As Dr. 
Bosanquet says, " a word means what it is used to 
mean, not what it once meant." ^ 

Sometimes the difficulty is increased by the older 
meaning lingering on in one special department of 
thought and knowledge. De Morgan gives a good 
example : " The word publication has gradually 
changed its meaning, except in the courts of law. It 
stood for communication to others without reference 
^ Logic, vol. 1, p. 52. 



Ambigui- 
ties in 
Individual 
Words. 



56 THE LOGICAL BASES OF EDUCATION chap. 

to the mode of communication, or the number of 
recipients. Gradually, as printing became the 
easiest and most usual mode of publication, the 
word acquired its modern meaning ; if we say a man 
publishes his travels, we mean that he writes and 
prints a book descriptive of them. I suspect that 
many persons have come within the danger of the 
law, by not knowing that to write a letter which 
contains defamation, and to send it to another 
person to read, is publishing a libel ; that is, by 
imagining that they were safe from the consequences 
of publishing, so long as they did not print." ^ 

But when ambiguity arises from individual words it 
is generally due to doubt as to which of various current 
meanings is intended. Such instances of ambiguity 
are especially common in the sciences which deal with 
man's life. These naturally have very few technical 
terms, but use the words of common speech with all 
their vast flexibility of meaning. The door is thus 
opened wide to misconceptions of meaning. A 
writer intends to use a word — say such a term 
as ' money ' or ' value,' or ' motive ' — in one 
sense, and is, it may be, careful to state his 
intention explicitly. But his reader may forget 
this limitation and read another sense into the 
word, and so misunderstand him. Indeed, words 
which are used in widely differing senses are a 
pitfall to the writer himself. He is liable when 
using such a term in one sense to make assertions 
or to draw inferences which are only justified 
when the term is used in another sense. For 
example, when ' money ' is said to be ' ;%sarce ' 
in the money market, the meaning is that there is a 
scarcity of capital seeking investment. To infer 
from this that the coinage of gold and silver coins 
^ Formal Logic, p. 243. 



ni KNOWLEDGE AND LANGUAGE 57 

should be increased is to be misled by the fact that 
in another meaning ' money ' is limited to such coin- 
age. But ' scarcity of money ' in the former sense 
is by no means the same thing as ' scarcity of 
money ' in the latter sense, and has no necessary 
connexion with it. 

Another ambiguous word is ' government.' 
Suppose we are asked whether it is ever lawful 
to resist the government. Our answer must depend 
upon whether by ' government ' is meant the 
system of laws established in a nation or the body of 
men charged with carrying out those laws. It may 
happen that the government in the latter sense is 
trying to subvert the government in the former 
sense. In that case, in whichever way a man acts, 
he resists the government in one of the two senses 
of the word, and what is loyalty from the one point 
of view is disloyalty from the other. 

' Nature ' is another very ambiguous word, and 
particularly so when used in the attractive phrase, 
"education according to nature." This has meant 
very different things with different writers. With 
Comenius it meant that educational method should 
be based on more or less fanciful analogies with 
processes in the physical world. For example : " The 
sun does not occupy itself with any single object, 
animal, or tree ; but lights and warms the whole 
earth at once. ... In imitation of this there should 
only be one teacher in each school, or, at any rate, 
in each class." ^ Rousseau first made the phrase 
really fashionable. With him and his followers it 
mean-*- that the educator should mainly look on, 
whilst the child follows his innate impulses. The 
perfection of manhood was held to be discoverable 

^ The Cheat Didactic (Keatinge's Translation), pp. 315 — 
316. 



58 THE LOGICAL BASES OF EDUCATION chap. 

only in "the noble savage," before the dawn of 
civilization had corrupted humanity. A similar 
thought underlies the excuse so frequently given for 
not checking childish faults, that they are ' natural.' 
On the other hand, Plato and many modern thinkers 
regard man's true nature as the ideal perfection 
towards which all advance in real civilization is a 
slow and toilsome struggle. They seek true human 
nature in the end of man's development, not in the 
beginning of it. With them " education according 
to nature " means guiding the child along the path 
of this development as far as his capacity will allow. It 
is evident that such opposed interpretations of the one 
phrase will lead to very different educational systems. 

No words cause more ambiguity than pronouns, 
because their reference is always decided nearly 
entirely by the context. Any number of examples 
can be culled from even our best writers. For 
instance, Steele writes : " When a man considers the 
state of his own mind, he will find that the best 
defence against vice is preserving the worthiest 
part of his own spirit pure from any great offence 
against it," i where the reference of "it" is by no 
means clear. 

A great daily newspaper, in describing the at- 
tempts made to discover the robbers of a large 
sum of money from a London bank, told its readers 
" The bank is well guarded. Officials are specially 
employed to watch all transactions from places where 
they are not seen." ^ If the reference of "they' is 
to be decided by grammatical rules, the authorities 
who placed the officials would seem to have acted 
with much unwisdom. But probably the writer did 
not mean what he said. 

1 Guardian, No. 19. 

- The Daily Chronicle, January 26th, 1899. 



Ill KNOWLEDGE AND LANGUAGE 59 

Not nouns and pronouns only, but any part of 
speech is liable to be ambiguous. Swift speaks of 
"the Reformation of Luther," where the "of" is 
probably meant to be equivalent to " by " In the 
Spectator we read " I have long since learned to like 
nothing but what you do," where the ambiguity of 
the last word is very apparent. The dentist who 
advertised : " Teeth extracted with great pains," was 
- not only ambiguous in expression, but — probably 
unconsciously — humorous. 

An important cause of ambiguity is the fact that 
words such as ' all ' and ' some ' can be used either 
collectively or distributively. "I can move all 
those books," may be true if they may be moved in 
succession, but false if they are to be moved in a body. 
The spendthrift argues " I can afford this, or that, 
or the other," and draws the conclusion that he can 
afford them all collectively, to the ultimate grief of 
his creditors. On the other hand, the miser is prone 
to urge that because he cannot afford to subscribe 
to all the socially useful institutions that beg his 
help, he therefore cannot afford to subscribe to any. 
Schools are especially liable to suffer from false 
inferences due to ambiguity of this kind. Many 
excellent people see in the study of some particular 
subject a sovereign cure for all educational ills, and 
urge the inclusion of that subject in the curriculum 
of every school. Unhappily each doctor has a 
different quack remedy, and though time and energy 
might be found for including any one, yet the at- 
tempt to include all leads only to disaster. How- 
ever, each reformer urges that room can be found 
for his own pet subject, and the educational lawgivers 
are too apt to yield in every case, through looking at 
the question piecemeal instead of as a whole. 

Misconception or doubt as to meaning arises even 



60 THE LOGICAL BASES OF EDUCATION chap. 

more frequently from clumsily constructed sentences 
than from doubt as to the meaning of individual 
words. Indeed, the former is the common cause of 
the latter, as is apparent in the few examples we 
have given, and as might be expected from the fact 
that alteration in the meaning of a word is mainly a 
matter of context. In an analytic language like English 
the meaning depends on the order of words much 
more than in a synthetic language like Latin. Am- 
biguity is frequently due to want of care in locating 
words and phrases. Here again numerous instances 
can be found in even the best writers. Says Swift 
in Gulliver's Travels, " It contained a warrant for 
conducting me and my retinue to Traldragdubb or 
Trildrogdrib, for it is pronounced both ways, as near 
as I can remember, by a party of ten horse," where 
we get at the meaning only by mentally transposing 
the last phrase, on the assumption that the writer 
must have meant something different from what he 
said. In his translation of Homer's Odyssey Pope 
tells us " And thus the son the fervent sire addressed," 
which is as ambiguous as is the line " The noble 
hound the wolf hath slain " in W. R. Spencer's poem 
Gelert. " An instance of [ambiguous construction] 
maybe read on the walls of Windsor Castle — 'Hoc fecit 
Wykeham.' The king was incensed with the bishop for 
daring to record that he made the tower, but the 
latter adroitly replied that what he really meant to 
indicate was that the tower was the making of him."^ 
In the Tatler, Steele writes " He had by some strange 
magic arrived at the value of half a plumb, as the 
citizens call an hundred thousand pounds," ^ leaving 
his readers to wonder whether the sum mentioned 
was, in the slang of the day, " a plumb " or " half a 
plumb." Many ambiguous constructions are uncon- 
1 Stock, Deductive Logic, p. 303. ^ Tatler, No. 40. 



Ill KNOWLEDGE AND LANGUAGE 61 

sciously humorous. Perhaps as good an example as 
could easily be found was furnished by a pushing 
shopkeeper in one of our great northern towns who 
exhibited in his window, to the joy of all beholders, 
a placard bearing, in all the emphasis of large type, 
the legend " Why go elsewhere to be cheated 1 
Come in here ! " 

The haste in which much modern writing is done, 
especially for the daily press, causes such slip-shod 
sentences to be presented again and again to the 
reading public. The natural result is that careless- 
ness in expressing thought spreads, and we have 
continually to " read between the lines " to get at an 
author's meaning. Doubt has, indeed, been expressed 
whether the majority of Englishmen ever either say 
what they mean or mean what they say. This is 
undoubtedly much to be regretted. When the close 
connexion of speech and thought is considered it 
becomes evident that looseness of expression is sure 
to react more or less on thought. Indeed, it is 
continually found that ambiguities such as we have 
been considering are the root from which spring many 
of the fallacies, or erroneous interpretations and infer- 
ences, which meet us on every hand. The educator 
can engage in few more useful tasks than that of 
training his pupils to clear and exact expression of 
meaning. 



CHAPTER IV 

KNOWLEDGE AND LOGIC 

Nature of § 1. — KNOWLEDGE, as we have Seen, can only 
Logic. include beliefs of mankind which are true, that is, 
which agree with reality ; in knowledge, belief is in 
harmony with fact. But to say this would be 
without meaning if we were una^ble to distinguish 
genuine from apparent knowledge. To say we ' know' 
therefore implies that we can know that we know ; 
in other words, that knowledge itself can be an 
object of knowledge. And this is possible because 
knowledge is a part of reality ; it is an important 
factor in the one universe, or totality of existence, 
which is the object of all knowledge. If, however, 
it is possible to distinguish knowledge from mere 
belief, there must be certain general conditions which 
are found in all cases of knowledge, and are absent 
from all cases of mere belief. The investigation of 
these conditions is the province of logic. 

Again, we have seen that knowledge itself is in a 
state of continuous growth and development, and 
that the knowledge of mankind is both the product 
and the corrective of the knowledge of individuals. In 
order to examine the nature of knowledge, then, it is 
not sufficient to study the structure of the whole of 



CH. IV KNOWLEDGE AND LOGIC 63 

knowledge as it is, it is necessar'y also to enquire into 
the conditions of its growth and development, both 
in the individual and in the race. Just as botany 
considers not only the structure but the growth and 
development of plants, and geology investigates not 
only the nature of the earth's crust but the processes 
which have given to that crust its present form, so 
Logic is the science which investigates the origin, 
development and structure of knowledge. 

§ 2. — All knowledge and all belief exist in the Nature of 
form of judgments or assertions. The assertion J^^'^^'^ient. 
may be merely mental, and it need not be fully and 
explicitly set out in words. But every attempt 'at 
interpreting experience is an assertion or judgment . 
of some kind ; for, as has been shown in the pre- 
ceding chapters, it is a reference of an idea to reality, 
and such reference is exactly what is meant by 
judgment or assertion. It follows that judgments 
are of varying scope, corresponding to the different 
extent of the ideas or systems which represent our 
mental construction of reality. From the widest of 
all possible judgments, which asserts the universe as 
a systematic whole, to the interpretation of a simple 
present experience, such as "it rains "or "I have a 
toothache," the gradations are innumerable, but the 
difference of scope does not affect the essential 
character of the mental act. 

§ 3. — Now, about every assertion the fundamental Judgments 
questions to be asked are : What does it mean 1 On 
what evidence is it based ? Is it true 1 On the 
answers which can be given to these questions in 
any particular case depends the decision whether the 
judgment in question is to be admitted as a piece of 
knowledge. 

It is not, however, with the meaning and truth of 
this or that particular judgment that logic is 



64 THE LOGICAL BASES OF EDUCATION Chap. 

concerned, but with the conditions of the validity of 
judgment in general. • Whether those conditions 
are fulfilled in any particular case must be left for 
decision to that branch of science v/liich enquires into 
the special subject-matter with which the judgment 
deals. Hence it is about judgments in general that 
logic asks the questions which the special sciences 
ask about particular judgments. 
Abstract § 4, — This makcs it plain that logic is a very 

Nature of ^ . »n . • i t • i c 

Thought, abstract science. All science, indeed, is abstract, tor 
each science is the construction of reality from one 
special point of view. It is only by approaching 
reality now from this side, and now from that, that 
•human thought can deal with it at all. " The mind, 
with all its powers, is incapable of grasping the 
whole even of the ' flower in the crannied wall.' ^ It 
deals with it first under this aspect, and then under 
that — as a thing of beauty, as suggestive of a 
Wordsworthian sonnet, as injurious to the structure 
of the wall, as a Comjyosita, as consisting mainly of 
carbon, oxygen, hydrogen, and nitrogen in certain 
proportions, as decomposing so many cubic feet of 
carbonic acid per diem under the influence of sunlight. 
And whichever aspect we like to take we are pretty 
sure to leave out the rest. The sonnet would be 
deranged by a thought of the carbonic acid. And 
yet somehow all these aspects belong to the flower. 
The whole, which is the real, contains or presents 
them all and many more. And so we learn our first 
lesson about thought, that to grasp anything at all 
we must leave out the greater part of it. . . . We 
must admit that the mind never yet sifted out a 
grain of truth without letting twenty other grains 
slip past unnoticed." ^ 

1 Cf. p. 19. 

2 Hobhouse, The Theory of Knowledge, pp. 6—7. 



IV KNOWLEDGE AND LOGIC 65 

To know even the smallest piece of reality at all 
thoroughly, we have, then, to think it successively 
under a great number of general ideas, each of 
which includes under it a vast number of other 
particular facts. Every general idea is thus the 
expression of a relation binding together a vast 
number of individuals ; it is the universal identity 
which exists amidst the particular differences of the 
individual facts. Each general idea is also related 
to other general ideas dealing with similar aspects of 
reality, and thus we get those organized systems of 
knowledge which we call the ' sciences.' It is 
evident, then, that every fact may be considered 
from the point of view of many sciences, each of 
which deals with it from one side. This is just what 
is meant by saying the fact is concrete, and the 
science abstract. The concrete means simply the 
embodiment of a number of general qualities or 
relations ; the abstract means simply the selection of 
one of those aspects and the exclusion of the others. 

§ 5. — This distinction is closely connected with Form and 
that betweenybrm and matter. The simplest example 
of ' form ' is the shape of a material object, say a 
statue, whilst the ' matter ' is the marble, bronze, or 
other material of which it is composed. Here we see 
at once that the form is the creation of man's mind ; 
it is that which gives artistic value to the statue, 
indeed, that which makes it a statue at all as dis- 
tinguished from a mere block of stone or metal. 
This, however, is only a first application of the terms. 
Further thought shows that the same distinction can 
be applied throughout. " There is no matter without 
form ... In a knife the matter is steel, the form 
is the shape of the blade. But the qualities of steel 
again depend, we must suppose, upon a certain char- 
acter and arrangement in its particles, and this is, as 

F 



Matter. 



66 THE LOGICAL BASES OF EDUCATION chap. 

Bacon would have called it, the form, of steel. But 
taken as purely relative, the distinction is goo^ prima 
facie. Steel has its own form, but the knife has its 
form, and the matter steel can take many other forms 
besides that of a knife. Marble has its own form, 
its definable properties as marble (chemical and 
mechanical), but in a statue, marble is the matter, 
and the form is the shape given by the sculptor." ^ 
Similarly, we may say that a mathematical formula 
is the form, of which the particular examples which 
come under it are the matter. 

But just as there can be no matter without form, 
so there can be no form without matter. Nor is the 
form independent of the matter. Many forms which 
can be expressed in gold cannot exist in clay, in sand, 
or in water. The form each material can take is 
partly determined by its own nature^ and is one way 
in which that nature is expressed. 

§ 6. — The ' form ' then of any piece of reality con- 
sists of the general abstract qualities and relations 
which it exemplifies. Thus every science deals with 
one particular ' form,' or kind of qualities and rela- 
tions, and the more general those qualities and rela- 
tions are the more emphatically 'formal' is the science. 
Thus, mathematics is one of the most formal and 
abstract of sciences, as it deals with an aspect of all 
things which can have quantity. But logic is yet 
more formal, as it deals with the form of all know- 
ledge, that is with those most general conditions which 
differentiate knowledge from what is not knowledge. 
As each science neglects every aspect of reality but 
one, so logic neglects all aspects of actual knowledge 
except those which belong to it simply as knowledge, 
irrespective of the reality which is known. It deals 
"not with the results of knowledge, but with the 
^ Bosanquet, Essentials of Logic, p. 43. 



IV KNOWLEDGE AND LOGIC 67 

outline plan upon which these results may ultimately 
be put together."^ 

Thus, logic has to find its subject matter, not in 
the external world of sense-experience, but in the 
world of thought. Its subject matter is, in a sense, 
not new ; for in studying knov/ledge we are neces- 
sarily dealing with the same objects of knowledge 
with which we deal in other sciences. The difierence 
is that in the other sciences we deal with these objects 
as they are in themselves and in relation to each other, 
whilst in logic we deal with them merely as examples 
of how we know, that is, in a certain relation to our 
own minds. In this logic resembles psychology. But 
in logic the emphasis is laid on the knowledge, whilst 
in psychology it is laid on the mind. In other words, 
logic is concerned with the validity of the thought, 
psychology only with the manner of its occurrence. 

§ 7. — But though logic considers the validity of Function 
thought it is not its function to teach men how to reason, ^^ ^°^^' 
" Men reasoned generation after generation long 
before they knew a single dialectical rule. . . . The 
principles of logic were operative in every ratiocina- 
tion, yet the reasoner was incognisant of their 
influence until Aristotle anatomized the process." ^ 
And nowadays men reason — and often reason well 
— who have never studied logic. Logic, in other 
words, does not lay down laws for thought, it does 
not set itself up to decide what methods of investiga- 
tion will lead to truth. In the Middle Ages logic 
pretended to do this, with the result that during the 
centuries when men accepted its guidance, knowledge 
made scarcely any advance. The logician nowadays 
is more modest. He sees that his province is to 
accept as valid all methods which lead to an increase 

^ Hobhonse, op. cit., p. 10. 
2 Ferrier, Institutes of Metaphysic, p. 15. 

F 2 



68 THE LOGICAL BASES OF EDUCATION ch. iv 

of knowledge, and to analyse them, so as to find out 
what is essential and what is accidental in them. 
Nor does he claim to dictate to the future. For just 
as sciences like botany and geology can speak with 
much more certainty of the form which development 
has taken up to the present than of the form it will 
take in the whole range of the future, so it is with 
logic. The logician can analyse the processes which 
have led to knowledge in the past, and are leading to 
knowledge in the present, but he must not attempt 
to limit the activity of thought by saying that those 
processes are the only ones which can ever lead to 
knowledge. 
Value of § 8. — The purpose of logic is, then, to make 
Logic, clear and explicit the principles and the character of 
valid thought; of thought, that is, which attains 
knowledge. And in this is its value. The person 
who has not studied logic has generally never made 
clear to his own mind the conditions which deter- 
mine the accuracy of his inferences. Many a man 
" infers, but can give you a very poor account of the 
grounds of his inference. He may, even so, infer 
well, in which case he is a person of insight, tact, 
skill, wisdom, but not a reasoner, nor one who 
understands the logical connexion of things. The 
practical mark of such a person is the irregularity 
of his success in inference. He reasons well when 
he has great experience or some natural gift, but 
apart from that he flounders. A logical mind is 
slower but surer." ^ The study of logic aids in the 
cultivation of the logical mind, though it will not 
ensure its development. By making clear the 
principles on which correct thought proceeds, logic 
indirect!}^ helps the production of correct thought, for 
those principles can be consciously accepted as guides. 
'>■ Hobhouse, op. ciL, pp. 2S7 — 238. 



CHAPTER Y 

NATURE OF JUDGMENT 

§ 1. — We have seen that every piece of know- Judgment 
ledge and of belief exists in the form of judgment Propositior 
or mental assertion, and further that about every judg- > 
ment we should ask the three fundamental questions 1 
as to its meaning, its truth, and its justification.^ / 
We have now to deal with the j&rst of these questions / 
in that general way in which alone logic is con- 
cerned with them. We have to enquire what is 
involved in the act of judgment as such, and what, 
consequently is implied by every judgment, no 
matter what the subject is with which it deals. 

In entering on this enquiry it must be borne in 
mind that it is judgment as a mental act, and not 
the proposition, or form of words in which it may 
be expressed, with which we are primarily con- 
cerned. We can only consider judgments when 
they are verbally expressed, but this expression is 
very often imperfect, and in such cases we must go 
behind the proposition to find the true judgment, 
and having found it we are at liberty to express it 
in another verbal form if in that way we can state 
1 See p. 63. 



70 THE LOGICAL BASES OF EDUCATION chap. 

the real meaning more clearly. Logic, indeed, postu- 
lates that expression must be adapted to thought. 
Of course, we only know the judgments of others 
through the propositions in which they are presented 
to us, but we can frequently see that the verbal 
presentation does not precisely coincide with the 
judgment it is intended to express. We have, 
then, to interpret the verbal expressions of other 
people's thought just as much as other pieces of 
our experience. Sometimes, no doubt, our inter- 
pretation is wrong, and then the judgment conveyed 
to our mind is different from that which existed in 
the mind of the speaker or writer from whom we 
received the proposition, and we have a case of mis- 
understanding. 

Having decided what judgment a given proposi- 
tion conveys, we must either accept it, reject it, or be 
in doubt about it. In the last case we do not our- 
selves judge about the matter at all ; we suspend 
judgment. But both when we accept and when we 
reject a proposition offered us by another, we our- 
selves perform an act of judgment. In the one case 
we adopt the suggested judgment as our own; in 
the other case in rejecting the suggested judgment 
we of necessity accept its contradictory; if, for 
example, we reject the judgment that war is some- 
times necessary we by that very rejection mentally 
aflSrm — i.e., we judge — that war is never necessary.^ 
Judgment § 2. — This has led us to one essential characteristic 
of judgment as a mental act ; it always claims to be 
true. It is impossible for any one to judge what he 
believes to be false. Any one judgment may of 
course be actually untrue; but it cannot appear 
untrue to him who makes it at the moment when he 
makes it. A judgment, then, may be a truth or a 
1 Of. p. 29-30. 



and Truth. 



V NATURE OF JUDGMENT 71 

falsity, but it cannot be a falsehood. A proposition 
may, of course, be a falsehood, and it may even be a 
falsehood when it is true, for he who utters it may 
believe it to be false and so to him it is a falsehood. 
But this is an ethical and psychological consideration, 
not a logical one. Logically we are concerned, not 
with whether a person who makes a statement actually 
believes it, but with whether it is in reality true or 
false. The question of intention has no interest for 
logic, but only the question of actual truth or falsity ; 
and this is a question which applies to every judg- 
ment and to every proposition. 

This claim to truth makes it clear that every sen- 
tence is not a proposition. A sentence may express 
a command, a wish, or a question. But to command 
or to wish a thing does not necessarily make it true 
or real — " If wishes were horses, beggars would ride." 
However, the command or the wish exists truly 
enough in the mind, though its accomplishment may 
never become a reality in the world of hard fact. 
Hence, every command or wish may be taken as an 
indirect expression of a judgment concerning the 
desires of him who makes it ; for instance, " Come 
here, John," is an indirect way of expressing the 
judgment "My wish (or intention) is that John 
should come here." Similarly, a question is not a judg- 
ment ; indeed it indicates the absence of the power of 
judging in some particular about the matter with 
which the question deals. But indirectly it may be 
taken to express a judgment as to the mental state 
of the questioner — the judgment that he is ignorant 
a,nd desires information on a certain point. 

Further, nothing but a judgment can be true or 
false. We say sometimes " Nothing can be truer than 
fact," but by fact we do not mean simply an occurrence 
in the external world but such an occurrence as 



and Ex 
perience 



72 THE LOGICAL BASES OF EDUCATION chap. 

known; i.e., as judged. The occurrence simply ^5 ;/ 
it is the judgment about it which is true or false. / 
Judgment § 3. — Whenever we judge, then, whether our 
judgment is original or whether it is the acceptance 
of a judgment offered us by another, we assert what 
we believe to be true. And such assertion is not 
arbitrary, it has behind it what seems to us a 
sufficient ground — a ground which would compel any 
other rational mind to make the same judgment. 
The question of when such ground is really sufficient 
will occupy us in future chapters : we only point out / 
now that to judge without any grounds is impossible/ 
to a rational mind. ' 

Of necessity, the grounds for every judgment must 
be found in the apprehended nature of that with 
which the judgment is concerned. To say a judg- 
ment is true is to say it represents reality. But, as 
we have seen, reality exists for man only so far as he 
is aware of it ; he interprets it in the form of judg- 
ment and in that form only.^ Every separate judg- 
ment is, then, an attempt — believed at the time to be 
a valid attempt — mentally to reconstruct reality, that 
is, to construct in our thought a system corresponding 
to actual existence. Every such attempt is occasioned 
by some experience, for it is only in experience that 
reality is known. Every piece of experience must be 
interpreted, or made intelligible, before it can take its 
place in our system of knowledge. Such interpreta- 
tion harmonizes that experience with the system of 
knowledge already existing and derived from other 
experiences, either of ourselves or of others. 

But our systems of knowledge exist in the form 

of ideas. ^ Interpretation of any experience is, then, 

the bringing it under some idea, that is, the seeing it 

as an example of the general nature or law which that 

^ Cf. pp. 27, 63. 2 cf. p. 42. 



V NATURE OF JUDGMENT 73 

idea embodies. It must not be forgotten, however, 
that the idea is itself a part of reahty and is derived 
from the reahty it more or less truly represents. 
Ideas are not made by the mind outside of experience 
and independently of reality. Their content is i 
found by us in reality; but found by thought I 
and not by the exercise of the senses of seeing, hear- / 
ing, &c. Experience is the whole of mental life, - 
and includes our interpretation of what comes to us 
through the senses as well as those sense-impressions 
themselves. If we remember this, then we can 
truly say that all knowledge is experience, but if we 
make the very common mistake of limiting " experi- 
ence " to sense-impressions, then such a statement 
becomes absolutely absurd, for sense-impressions 
are not knowledge at all, but only the materials 
out of which the mind makes knowledge. 

§ 4. — In every judgment, then, we interpret Judgment 
some piece of experience by referring it to an idea of both 
derived from previous experiences. But the piece of ^nd ^^^^ 
experience we interpret is never the whole of our Synthesis. 
experience at the moment ; it is some element in that 
whole selected by attention. If I say, " This room is 
too warm," I am fixing attention not merely upon my 
space surroundings, but upon one aspect of those 
surroundings, and by so doing I am neglecting the 
rest. There are other aspects of the room besides 
its temperature to which I could attend, but I am 
led by my feelings, or by some purpose, to attend only 
to the warmth. The judgment is, then, an act of 
analysis, or of selection of some elements out of a 
totality to the neglect of the rest. In other words, | 
the judgment actually made is only one of a large / 
number of judgments which could be made about 
the room ; " warmth " is only one of the ideas under 
which it could be regarded. Every judgment, then. 



74 THE LOGICAL BASES OF EDUCATION chap. 

is merely a partial interpretation of experience ; we 
can only master reality bit by bit.^ 

The judgment is an act of analysis in a further 
sense. The too high temperature is one experience 
which forces itself upon my attention. When 
attended to, it is resolved into the two ideas of the 
temperature of the room, and of excessive warmth 
as a quality of that temperature. It is the actual 
room-temperature which is experienced by the senses ; 
its effect on me is explained by bringing that tempera- 
ture under the idea of excessive warmth. So in every 
case. We see a bird flying, and the bird and its 
flight are one and the same experience, and the 
judgment which expresses that experience is.- one 
simple act of thought. But it is an act which 
analyses the experience into the two elements of bird 
and act of flying, and asserts that the latter is true 
of the former. 

This is, however, only one side of the truth. Each 
of the two parts into which a judgment analyses an 
experience has a meaning by itself, and these mean- 
ings are not identical with each other. We can 
think of birds in many other acts besides that of 
flying ; and we can think of flying as the movement 
of kites and arrows as well as of birds, or of other 
birds besides this particular individual. The judg- 
ment is an act of synthesis, or building up, as well 
as an act of analysis, or taking to pieces. The two 
general ideas of bird and flight are thought together 
and modify each other. 

Every judgment is, then, an act both of analysis and 
of synthesis. The fact that judgments can only be 
examined in the form of propositions tends, however, 
to cause the analytic aspect of the act to be overlooked. 
For the proposition is composed of words, each of 
1 Cf. p. 64. 



V NATURE OF JUDGMENT 75 

which is a separate element in that proposition, and 
these words must be both produced and received 
successively. Hence there arises a tendency to regard 
a judgment as a synthesis only. Because in the pro- 
position " The bird flies '' the words " the bird " must 
be both uttered and heard before the word "flies,"- 
and because he who hears the statement must gather 
its meaning by putting together these two ideas, 
it is assumed that this is a sufiicient account of 
the judgment. But it is not so. The judgment 
originated in the analysis of an act of perception, and 
when it is communicated to another, it only becomes 
a judgment to him when bhe whole is grasped, so that 
the elements are no longer separate but are seen as 
connected in that whole, and, therefore, stand before 
the mind as the results of an analysis of that wdiole. 
It must be always borne in mind that the proposition 
or verbal statement is only instrumental to the judg- 
ment, and that in the latter the two essential parts, 
though they are distinguished, are not separated as 
are the words in a sentence. 

§ 5. — We have, then, two essential parts in a 
judgment, and these are called the Subject and 
the Predicate, The same two terms are used in 
grammar, but the grammatical subject is not always 
the logical subject. By the latter is meant that part 
of the experience interpreted from which the thought 
starts j and by the logical predicate is meant that 
further movement of thought which makes the 
experience more explicit. In isolated judgments it 
is frequently impossible to say with certainty what 
is the logical subject. Take the sentence " This is 
an orchid." This may be an answer to an enquiry 
as to which of certain plants is an orchid, when the 
subject would be " an orchid," and the predicate would 
be the indication of a particular flower, this indication 



76 THE LOGICAL BASES OF EDUCATION chap. 

being verbally represented by the word " this." But 
on the other hand the same sentence may be an 
answer to the question " What is this flower 1 " and 
in that case the " this " represents the subject, for it 
is the starting point of the thought, and " an orchid " 
is the predicate, for it is the further filling out of 
that thought. Similarly, the limits of the logical 
subject depend on what is already known. " If you 
say, ' He is going down to Yorkshire to-morrow by 
the 9*45 from King's Cross,' you divide 'he' as 
the grammatical subject from the rest as predicate ; 
but the real transition in thought is from what we 
knew before to what the judgment tells us, and on 
this principle we might divide the judgment at any 
point, and should do so if we wish to represent the 
character of the advance, according to the interest 
which the statement satisfies — 'He,' or 'going,' or 
' Yorkshire,' or 'the 9 "45 ' or 'King's Cross,' may be 
the real predicate, the real addition to what we knew 
before." ^ This shows that the actual determination 
of subject and predicate in any case is psychological. 
There is always a logical subject and a logical 
predicate, but these are not fixed elements. " The 
content of the judgment is a complex of inter- 
connected elements, any one of which can stand as 
subject or as predicate to the rest." ^ It is evident, 
then, that the ' grammatical subject ' — that is, the 
nominative to the principal verb — cannot in any 
proposition be taken, without further enquiry, as the 
logical subject. But yet, as speech should exj)ress 
thought with the greatest possible exactness, judg- 
ments are most adequately represented by propositions 
in which there is this coincidence, so that, as Dr. 
Bosanquet puts it : "I think that to ask whether 
the grammatical corresponds to the logical subject is 
^ Hobhouse, The Theory of Knoivledge, p. 156. ^ ji^^^^ 



V NATURE OF JUDGMENT 77 

only to ask whether we have said what we meant to 
say." 1 

§ 6. — We have, however, yet another element of Copula. 
the proposition to examine. Logic prefers to express 
judgments by propositions in which subject and 
predicate are separated by the verb ' is ' or ' are,' 
with or without the negative 'not.' Thus, the form 
" Gold is lustrous " would be preferred to the form 
"Gold glitters." This additional element in the 
expression of a judgment is called the Copula, and 
always consists of the present tense of the verb ' to 
be.' Now the word " copula" suggests the idea of a 
link joining two independent ideas; and then the 
analytic aspect of the judgment is lost sight of. So 
fully is this sometimes done that Mr. Swinburne in 
his Picture Logic represents subject and predicate as 
two railway carriages, and the copula as the coupling 
chain attaching them to each other.^ "This," as 
Dr. Bosanquet remarks, "is an excellent type of the 
way in which we should not think of it."^ The 
copula is, indeed, not an independent element of the 
judgment at all, and its function in the proposition 
is only to indicate that the act of judgment has 
really taken place. " Benno Erdmann has strikingly 
expressed this point of view by saying, that in the 
judgment, ' The dead ride fast,' the subject is ' the 
dead,' the predicate ' fast riding,' and the copula ' the 
fast riding of the dead J '' * 

The copula is, then, a sign of judgment ; it is not 
a mere link joining two independent elements ; it 
does not add on to the subject a new idea which 
had previously no connexion with it, but it declares 

^ Knowledge and Reality, p. 183. 
2 Picture Logic, p. 173. 
^ Essentials of Logic, p. 100 (note). 
^ Bosanquet, op. cit., p. 100. 



78 



THE LOGICAL BASES OF EDUCATION chap. 



that subject and predicate are connected elements in 
one whole which the act of judgment has analysed. 
It is, therefore, a sign of both that analysis and 
synthesis which are aspects of every judgment. 

§ 7. — Though every judgment is both an analysis 
and a synthesis, yet either of these aspects may be 
the more prominent. It all depends upon whether 
the thought starts from the whole, and proceeds to 
make explicit the relations of the parts within that 
whole, when the analytic aspect is the more promi- 
nent ; or whether it starts from the parts as distinct 
and proceeds to bring out their connexion wifch each 
other, thus constituting the whole, when the syn- 
thesis is the more apparent. Simple examples can 
be found in such judgments as 8 = 5 + 3 where the 
analysis is the more prominent ; and in 5 + 3 = 8 
where the synthesis predominates. The fact is the 
same in each case, though the ways of approaching 
it are different ; and reality is not affected by the 
way we state it. This question, however, cannot be 
fully discussed at this stage ; all we would insist on 
now is that, as in each case both a whole and its 
connected parts enter into the judgment, and as 
they are distinguished but not separate in the act of 
judging, so in each, case the judgment is both an 
analysis and a synthesis. 

§ 8. — If now we sum up the results we have 
reached in this chapter, we may say : That judg- 
ment is coextensive with affirmation and denial ; that 
every judgment is a truth or falsity, but from its very 
nature claims to be true ; that truth means correct 
interpretation of the reality given in experience ;1 
that every judgment is a single act of thought, and 
is both analytic and synthetic, though one of these 
aspects may preponderate ; that the copula is not a 
link joining separate ideas, but is a sign that subject 



V NATURE OF JUDGMENT 79 

and predicate have been distinguished as connected 
elements in a given whole ; that the distinction of 
subject and predicate is not a fixed one, but is 
relative to the actual work of thought in the judg- 
ment ; that the proposition should be as exact a verbal 
presentment of the judgment as possible. 



CHAPTER YI 



TYPES OF JUDGMENT 



Main Types § 1. — A COMPLETE enumeration of the forms of 
ment*^^ verbal statement in which judgments are expressed 
is obviously impossible, and even were it made it 
would be of rhetorical rather than of logical interest. 
But an enumeration of the main types of judgment 
is a much simpler matter, and, as was said in the 
last chapter, it is the judgment with which logic as 
a theory of knowledge is primarily concerned.' Logic 
deals with the proposition only as expressive of a 
judgment, and is, therefore, justified in reducing 
the multitudinous forms of statement of ordinary- 
speech to a few typical forms, so long as these forms 
are capable of expressing all essential differences in 
the mode of judging. 

There are, as was seen in our earlier chapters, three 
main stages in the organization of knowledge — the 
stages of perception of things, of appreciation of 
universal relations, and of conception of system. Of 
course, in the totality of the knowledge of each one 
of us individually, and of mankind as a whole, we can 
find examples of each stage. In some domains we 
are in the last stage, in some in the second, and in 



CH. VI TYPES OF JUDGMENT 81 

others only in the first. Corresponding to each stage 
is a typical form of judgment. There is first the 
Categorical Judgment, or judgment of fact, such as 
" This ink is black," or " All these boys have passed 
the Cambridge Local Examination." Secondly, there 
is the Hypothetical Judgment, the typical judgment 
of universal relation or law, such as "If water is 
cooled to a temperature of 32° F. under the pressure 
of one atmosphere, it freezes." Thirdly, there is the 
Disjunctive Judgment,ov typical judgment of system, as 
" Triangles are either equilateral, isosceles, or scalene." 
Stated thus, these seem to be strictly marked o£f from 
each other by their form. They are, however, only 
typical forms, and as knowledge makes no sudden 
jump from one stage to another, but developes gradu- 
ally, so the judgments in which knowledge is expressed 
merge gradually into each other. Especially is this 
the case with the categorical and hypothetical judg- 
ments, as might be expected from the fact that the 
same analysis of reality which gives us exact know- 
ledge of individual things makes plain the relations of 
those things to others. 

Further, we shall have to examine the force and 
extent of the important distinction between affirma- 
tion and denial. 

§ 2. — We have now to trace the development of Deveiop- 
these types of judgment from the simplest forms, jjfdgment- 
and to show their relation to each other. We wiM 
trace this development first in the affirmative forms, 
and then consider the meaning of the negative forms. 

The simplest cases of categorical judgment are impersonal 
those Impersonal Judgme7its which express the general ^"^™^'^^*- 
character of a nearly entirely unanalysed mass of 
present experience. They arise out of a mass of 
vague feeling, and analysis has only proceeded so far 
as to determine its general character. Such judg- 

G 



82 THE LOGICAL BASES OF EDUCATION chap- 

ments are exemplified by the " It hurts " or " How 
nice ! " of the child. Here the logical subject is the 
undifferentiated mass of present experience, and the 
whole force of the judgment practically rests in the 
predicate. We make similar judgments throughout 
life, e.g., "It rains," " It is foggy,"where the "it" which 
indicates the subject has the vaguest kind of general 
reference to the weather experiences of the moment. 

Closely allied to these are judgments which may 
be called Demonstrative, as they indicate, though they 
do not necessarily name, the element of reality which 
they interpret. In these cases there is frequently no 
formulation in words at all ; a demonstrative judg- 
ment is implied in the very simplest act of recognition, 
When such a judgment is explicitly stated in words, 
the logical subject is generally represented by some 
such demonstrative word as 'This,' 'That,' "Here, 
' Now,' as when one might say " Here is London," 
"This is an orchid," "Now's the day and now's the 
hour." 

When the analysis has been carried a step further, 
the new movement of thought starts from the result 
of such a judgment as we have just considered. The 
whole result of this judgment will now form the 
subject, and the new judgment will take such a form 
as " This book is very interesting " — which obviously 
assumes the judgment " This is a book." 

A further step in complexity is taken in what 
may be called the Judgment of Particular Relation, 
as "Brighton is to the south of London;" "This 
book is heavier than that ." In such cases the an- 
alysis of experience is deeper, and has given us two 
terms and the relation between them. 

So far the judgments we have considered deal 
primarily with facts in present perception, though in 
asserting the predicate of the subject they necessarily 



I 



Judgments, 



VI TYPES OF JUDGMENT 83 

pass beyond present perception and bring in an idea 
derived from previous experiences. In the last two 
examples, moreover, the subjects also have a reference 
beyond the present, as "this book," "London," and 
"Brighton," are thought as having a continued 
existence. 

More obvious still is this growing width of refer- Historical 
ence when the judgment is of what may be called 
a historical character, as when we say, " Caesar con- 
quered Gaul." Here the proper name represents a 
person, who did many actions which are united 
into that whole which we call a life by the fact 
that they were the actions of one individual. The 
personality is, therefore, a universal, or factor 
common to all those actions, and they are the 
different expressions in which the character of that 
universal becomes manifest. Such a judgment has, 
then, both an individual and a universal character, 
and it forms a kind of transition between the purely 
categorical judgments of fact and the judgments 
of universal relation or law which mark the next 
stage of knowledge. 

But the aim of thought is to reach universal 
judgments, that is, judgments which hold true of all 
cases of a similar kind. The first step in this direction 
is taken when a present experience is found to agree 
with a number of remembered past experiences. 
Hence arise all Judgments of Enumeration, such as 
" My holidays for the last five years have been spent 
in Devonshire." In such a judgment there has been 
a synthesis of remembered experiences with present 
experience. When the remembered experiences have 
been all alike, we can sum them up in the word 
" all," as when one might say " All my attempts to 
pass examinations have been successful." 

But memory construction, even when we take it 

G 2 



Judgments. 



84 THE LOGICAL BASES OF EDUCATION chap. 

in its widest sense as including the memories of the 
whole human race, can carry us no further ; it can 
never justify us in making assertions which pass beyond 
experience. How then are we to reach such a truly 
universal judgment as " All cows eat grass " 1 From 
our observation, even when supplemented by the 
testimony of others, we cannot be justified in as- 
serting more than "Some cows eat grass," for it 
is certain that cows not yet born have not been 
observed, to say nothing of innumerable cows in 
the past, and perhaps in the present, that have lived 
outside the observation of man. And it is equally 
certain that our judgment covers all those cows. 
No doubt uniformity of experience, especially when 
that experience is very extended, gives us a strong 
presumption in favour of universal agreement. But 
such presumption is not a logical justification; it 
strengthens belief, but does not convert it into 
knowledge. Before the discovery of Australia, un- 
contradicted experience justified the judgment " All 
swans hitherto known are white," but had the really 
universal judgment " All swans are white " been 
made, the black swans of Australia would have 
proved it to be unjustified. 

Mere observation, then, however extended it may 
be, can never give logical justification for a really 
universal judgment. Such justification is always a 
matter of inference, and is the work, not of sense- 
experience, but of thought. Suppose a beginner in 
geometry has found that if he inscribes a triangle 
in a semi-circle, with the diameter as its base, the 
angle which touches the circumference is a right-angle. 
He has certainly no reason for asserting that any 
triangle similarly inscribed in any semi-circle would 
exhibit the same characteristic. This idea might occur 
to him, and would be likely to do so if he so inscribed 



VI TYPES OF JUDGMENT 85 

several triangles in semi-circles and found that each 
had a right angle touching the circumference. But 
there is no limit to either the number of triangles 
that could be thus inscribed in any one semi-circle 
or the number of possible semi-circles, and no 
amount of observation and measuring could ever 
deal with them all, and so justify the judgment 
" Every triangle inscribed in a semi-circle with the 
diameter as its base has a right-angle touching the 
circumference." It is only when by inference from 
the known nature of semi-circle and triangle he 
has proved that this judgment must be true that 
he is justified in asserting it. 

What is true in this case is true in every case. Tin Generic 
The universal judgment of the general form " Every •^"*^^™^"^^- 
S is P " is true only because something in the nature 
of the reality the judgment interprets makes the 
conjunction of S and P a necessary one. True 
universality is a consequence of necessity. This 
necessary connexion of content is better expressed 
in the Generic Judgment, the general form of which 
is " S as such is. P." 

But when we reach this point we have passed 
beyond mere judgment of fact. The generic 
judgment is at once concrete and abstract. It is 
abstract in that it asserts a universal connexion of 
content without direct reference to the instances in 
which that connexion may be exemplified in reality. 
But it is concrete in that it assumes there are such 
instances, and so justifies the universal categorical 
judgment " Every S is P." 

If we develop the abstract side of the Generic TUHmw- 
Judgment we reach the Hypothetical Judgment, judgment, 
the general form of which is "If S is M it is P." 
The generic judgment implies that there is some- 
thing in the reality interpreted by it which makes 



86 THE LOGICAL BASES OF EDUCATION chap. 

the connexion of S and P a necessary one. The hypo- 
thetical judgment makes this condition explicit. 
We may say, "Water freezes at a temperature 
of 32° F," when we state a general relation as a 
fact. But this rests on the hypothetical " If 
water be exposed to a temperature of 32° F. it 
freezes," when the temperature is stated to be not 
merely coincident with the freezing but the essential 
condition under which it takes place. This challenges 
examination as to whether the statement of condition 
is adequate, and further analysis of the facts in this 
case shows that it is not, and that v/e must add 
" under ordinary atmospheric pressure," as a co- 
ordinate condition. 

Whether a judgment of universal relation is 
stated categorically or hypothetically is, therefore, 
mainly a matter of convenience, determined by the 
purpose with which the judgment is enunciated. 
Which is the real nature of the judgment cannot 
be decided by its mere verbal expression. Often, 
indeed, a judgment which is essentially hypothetical 
is expressed by a proposition which is. categorical in 
form, as in the familiar "Trespassers will be pro- 
secuted." This would hold true even if there never 
were any trespassers, and so it never received 
realization in fact. For the actual judgment is "If 
any persons trespass they will be prosecuted," and 
the underlying reality which this judgment par- 
tially expounds is that system of law and law-courts 
which makes a prosecution for trespass possible. 

In the pure categorical judgment the reference to 
reality is direct, and the judgment deals with the 
concrete facts of experience. In the generic judg- 
ment this reference to reality is indirect, in that it is 
implied rather than affirmed that instances exist 
which exhibit the connexion asserted. In the 



VI TYPES OF JUDGMENT 87 

hypothetical judgment this concrete reference disap- 
pears, and the judgment is purely abstract, and 
indifferent to whether the relation it asserts can be 
exemplified in real sensuous experience or not. The 
law of inertia, for example, asserts that, if all inter- 
fering conditions were removed, a motion once started 
would go on for ever. The fact that in the actual 
world of sense-experience perpetual motion can 
never be produced, because such interfering condi- 
tions as friction cannot be entirely removed, does not 
touch the truth of this law. Hypothetical judgments, 
then, do not directly express facts in the ordinary 
sense of that word ; but indirectly imply them. 
" Underlying [such judgments] there is the implied 
categorical judgment, ' Reality has a character, such 
that, supposing so and so the consequence will 
be so and so.' And if this implied assertion 
is true, then the hypothetical judgment is 
trae, although its terms may be not only unreal, but 
impossible. 'If a microscopic object-lens with 
a focal length of y^^ inch were used, its magni- 
fying power with an A eye-piece would be so many 
diameters.' This is a mere matter of calculation, 
and is unquestionably true, depending upon the effects 
of refraction upon the optical image. But I 
do not suppose that such an object-lens could be made, 
or used." ^ In another way the hypothetical judg- 
ment is highly abstract. Every such judgment deals 
with only one aspect of the reality it expresses, and 
many such judgments are necessary to express any 
whole concrete fact. 

As the generic judgment finds a concrete 

expression in the categorical judgment of " allness " 

so the hypothetical judgment can be represented 

by what may be called the Concrete Conditional 

^ Bosanquet, Essentials of Logic, p. 123. 



THE LOGICAL BASES OF EDUCATION chap. 



Proposition, whose general symbolic expression may 
be taken to be " Whenever any S is M that S is P," 
where the reference to cases in which the connexion 
is exemplified is much more direct. Of course this 
statement does not necessarily imply that real cases 
have ever been found, or even can be found, but the 
use of the " whenever " is misleading when no such 
cases are known to exist. 

Both the generic judgment, with its concrete 
expression in the universal categorical proposition, 
and the hypothetical judgment attain their most 
perfect form when they are reciprocal, that is, when 
not only does the predicate always accompany the 
subject, but when it is never found without the 
subject. In such cases it is also true that " Every P 
is S " and that " If S is P it is M." But without 
special proof, we can never assume that this is so. 
It is as true that every right-angled triangle can be 
inscribed in a semi-circle as it is that every triangle 
inscribed in a semi-circle with the diameter as its 
base is right-angled. Similarly, the 48th proposition 
of the First Book of Euclid is the converse or 
reciprocal of the 47th. But in every case such 
reciprocity has to be separately established ; it is 
not implied by the original judgment. 

The hypothetical judgment, then, explains the 
connexion of S and P by making explicit the 
condition M. But where, we may ask, are we to 
find a resting-place in our search for explanation ? 
If the connexion of S and P is conditioned by 
M, we may equally ask for the element which is the 
ground of the connexion of S and M. So long as 
we keep to mere symbols there can be no stopping- 
point in this regress. But when we consider the 
matter with which any judgment deals we can find 
a resting-place, at any rate of a temporary character. 



VI TYPES OF JUDGMENT 89 

Ultimately, as was shown in chapter ii, explanation 
can be complete, only when the whole universe is 
exhaustively known. Practically, however, we find 
sufficient explanation for our present purposes in 
seeing clearly the position of any fact or any law in 
one of those smaller systems into which, for our 
convenience, we divide the universe. To express the 
content of such a system is the function of the 
Disjunctive Judgment, whose general symbolic 
statement is " S is P, or Q, or , . , Z," where the 
number of alternative predicates is determined by 
the matter with which the judgment deals. 
Except in very simple cases it is obviously impossible 
to give concrete examples of such judgments. We 
may say *' Graduation at the University of London 
is in either arts, science, law, medicine, or music," 
and, provided that the enumeration of faculties in 
the university is complete, this expresses the system 
in question. Similarly we express an arithmetical 
system when we affirm " All numbers are either 
prime or capable of being analysed into factors." 
Such judgments evidently rest upon the Principle 
of Excluded Middle, just as the judgments we have 
previously considered are expressions of the Principle 
of Identity. 

In the perfect disjunctive judgment a system is 
completely and accurately expressed. In such a 
case the alternative predicates between them exhaust 
the whole system, and each is exclusive of all the 
others. The judgment imposes a necessity to 
choose in any particular instance amongst those 
alternatives, and in this necessity is found the basis 
for the sufficiency of the condition stated by the 
hypothetical judgment. For in a system perfectly 
expressed by the judgment " S is either P or Q " it 
is evident that " If S is not P it is Q," and " If S is P 



90 THE LOGICAL BASES OF EDUCATION chap. 

it is not Q "; and these involve "If S is not Q it is 
P," and " If S is Q it is not P." The disjunctive, 
therefore, implies the hypothetical. But it has also 
a categorical aspect. For though no particular fact 
S can be indifferently P or Q, but must be one or the 
other and that alone, yet P and Q are always 
themselves only divisions of a wider predicate which 
embraces them both, and v/hose scope they together 
exhaust. This wider predicate is fixed by the topic 
of thought in connexion with which the judgment 
is made. If, for example, P, Q . . . Z are colours, 
then the wider predicate is " colour," and of this P, 
Q . . . Z are differences. The attribution of this 
wider predicate to the subject shows the general nature 
of the system of reality which the disjunctive judg- 
ment expresses. 

Knowledge of system is, however, in many cases 
imperfect, and many judgments expressed in the 
disjunctive form do not fulfil all the conditions just 
laid down, just as many generic and hypothetical 
judgments fall short of the ideal of exact thought 
in that they are not reciprocal. The imperfections 
of the disjunctive judgment are either that the 
alternative predicates do not exhaust the whole 
realm of possibility, or that they do not exclude each 
other. In the former case we have not a real 
disjunctive judgment at all, but only a vague and 
indeterminate categorical judgment; for the very 
essence of disjunction is that from the denial of one 
alternative we can pass to the affirmation of the rest, 
so that by the successive denial of every alternative 
but one we can pass with certainty to the knowledge 
of the reality of that one. The latter case also 
indicates a defective knowledge of system, and, 
indeed, shows that in actual life the disjunctive form 
is used to express doubt as well as organized 



VI TYPES OF JUDGMENT 91 

knowledge. Our first example would justify the 
concrete judgment " All graduates of London have 
taken a degree in either arts, science, law, medicine, 
or music," and we know that any one person may 
have graduated in more than one faculty, and from 
that point of view we might afiirm that the 
alternative predicates in this judgment are not 
exclusive of each other. But the logical subject of 
the judgment is not graduates, but the constitution 
of the university so far as relates to the conferring 
of degrees. Thus regarded, it is seen at once that 
graduation in any one faculty is, as a particular act, 
exclusive of graduation in every other faculty. If 
an individual graduates in a plurality of faculties it 
must be on a plurality of occasions, each of which 
excludes the other. So it is in every true disjunctive 
judgment. In so far as the alternative predicates 
differ they exclude each other. But, as is seen in 
the above example, this exclusion may not apply 
to their relation to the grammatical subject, unless 
that is also the true logical subject. We must 
not, therefore, assume such exclusion from the mere 
form of the proposition. In other words, we must piot 
regard any given disjunctive proposition as involving 
the hypothetical "If S is P it is not Q," and "If 
S is Q it is not P," unless we have evidence that 
P and Q cannot coexist in any one instance of S. 

§ 3. — So far, we have limited the discussion to Negation. 
cases in which our universal assertions would stand 
the test of experience. We know, however, that 
this is not always the case. We meet with ex- 
ceptions to many statements which were at first 
thought to be general. Hence arise both negation 
and limitation of the scope of our judgments. We 
have all the force of negation whenever two judg- 
ments are made of the same subject which cannot 



92 THE LOGICAL BASES OF EDUCATION chap. 

both be true, because their predicates are incompatible 
with each other, as when " on a particular occasion 
during a . . . visit of the Empress of Germany to 
London, it became the duty of the reporters of the 
public journals to describe Her Imperial Majesty's 
dress. Subsequently the Globe collected the descrip- 
tions of the costume as they were given by different 
reporters, to this effect : The Times stated that the 
Empress was in ' gold brocade,' while, according to the 
Daily ISfews, she wore a ' sumptuous white silk dress.' 
The Standard, however, took another view : 'The 
Empress wore something which we trust it is not 
vulgar to call light mauve.' On the other hand, 
the Daily Chronicle was hardly in accord with any 
of the others : ' To us it seemed almost a sea-green, 
and yet there was now a cream and now an ivory 
sheen to it.' No wonder that the Globe asks em- 
phatically, ' What did the Empress wear ? ' " ^ Each 
of the judgments here quoted really negates all the 
others, because only one of them can possibly be 
true. No negation, however, appears on the face of 
any of these judgments. We get such explicit 
negation when the judgment takes the negative 
form, " S is not P." 

A consideration confined to this bare form would, 
however, lead us to a very wrong conception of the 
nature of negation and of its work in thought. For 
in form the negative judgment is bare denial, and 
the P is not limited to any system of predicates. 
The form would cover such a statement as " Virtue 
is not green," quite as well as "The dress of the 
Empress is not green." But it is obvious that of 
these two only the latter has any rational meaning. 
The former does not correspond to an act of thought 
at all ; in other words, it does not represent a real 
^ Rooper, School and Home Life, pp. 83 — 84. 



VI TYPES OF JUDGMENT 93 

judgment. As we have seen, every judgment is 
made under a certain limitation of reference which is 
made clear by the context in which it actually occurs. 
This is the same as saying that every judgment is 
made within a certain system. If the predicate 
is *' green," the system is that of colour, and only 
things occupying space can be coloured, for they only 
are visible. Consequently we can only rationally deny 
any particular colour of things which occupy space. 

Further, it has been shown that in this limitation 
to system is found the justification for our judg- 
ments, and that no judgment can be made without 
a ground. Denial must, therefore, rest upon some 
ground. But bare denial only expresses ignorance, 
and knowledge cannot be constructed out of ignor- 
ance. Denial always rests, then, on a positive 
ground, and this ground is the presence of something 
in the reality with which the judgment deals which 
is incompatible with the proposed predicate. We 
can rationally assert that S is not P only when we 
know more or less definitely that S is Q, and that Q 
cannot co-exist with P in the same subject. Our 
apprehension of Q may, indeed, be by no means 
explicit ; we may only feel sure that if S were to 
receive P it would cease to be itself, but we cannot 
feel this unless we believe there is something in S 
which excludes P, and this something is the Q of 
our symbolic statement. 

It appears, then, that every negation rests upon an 
implicit disjunctive judgment, and as a consequence 
that denial and. affirmation mutually imply each other. 
Every denial is based on an affirmation, and every 
affirmation negates all the other alternative and 
incompatible predicates in the system to which the 
judgment is limited. The use of the affirmative or 
the negative form shows which aspect is predominant 



94 THE LOGICAL BASES OF EDUCATION chap. 

in thought, and this is determined in general by 
the purpose with which the judgment is made. 

§ 4. — These considerations have also made plain 
that the true function of negation in the work of 
constructing knowledge is to show the limitations 
within which our affirmations should be confined. 

Suppose that in opposition to the universal cate- 
gorical proposition " Every S is P," an exception is 
proved to exist. We have then to grant that " this 
S at any rate is not P." But the original judgment 
was based upon the generic judgment " S as such is P," 
which had been supposed to be true. We must now, 
therefore, grant that " S need not be P." But if 
the original judgment rested on any real evidence at 
all, it has not been entirely disproved, but only limited 
in its scope. We can still say " S may be P," or 
with more direct reference to particular facts, " Some 
S's are P." The distinguishing feature of such a judg- 
ment is the indefiniteness of the reference to S. 
Similar forms arise from unanalysed experience. We 
have seen that mere uniformity of occurrence will not 
justify us in making the universal judgment " Every 
S is P," but it will justify us in making the 
particular judgment " Some S's are P." And when 
we do so, we use the word ' some ' without prejudice to 
the possibility that ' every ' would be true in fact. 
' Some ' means in such a case that our knowledge is 
professedly imperfect ; we know there are cases — one 
at least — in which S is P, but our knowledge of the 
nature of the reality thus expressed is insufficient to 
enable us to say whether every S is P. In other 
cases in which we use the word ' some,' we do intend 
to exclude 'all,' but this can only be assumed to be the 
case when the context makes it perfectly clear. For 
example, suppose on examining the tabulated results 
of an examination we found that certain candidates 



VI TYPES OF JUDGMENT 95 

had failed in mathematics. We could immediately 
affirm that 'some' candidates had so distinguished 
themselves. But it is conceivable that further examina- 
tion of the results might show that this ' some ' could 
with truth be expanded into ' all.' This discovery 
would not make the former judgment false, but only 
turn it from an indefinite into a definite assertion. 

So long, then, as we have nothing but the form to 
guide us, that is, whenever we have no context of 
knowledge to show that the ' some ' is meant to exclude 
* air, we must assume that ' some ' means " I am sure 
of at least one case, but I do not know how widely my 
judgment will apply." Even when the context shows 
that ' some ' is known not to be ' all ' as when we say 
" Some boys are idle and some are industrious," yet 
the range of application of these particular judgments 
is always indefinite. They cannot, therefore, be a 
resting place for thought in its search after knowledge. 
By their very form they challenge further enquiry. 
But as the universal judgment can only be reached 
by such an analysis of content as will lead to the 
generic or the hypothetical judgment, so the line our 
investigations must take to transmute the particular 
into the universal judgment is further and more 
accurate analysis of reality. This may result in 
the finding a condition M which necessitates P, and 
then we have the hypothetical "If S is M it is P," 
or the generic " S which is M is P," which are alter- 
native ways of expressing the same judgment. 

It is, indeed, in some such process of finding ex- 
ceptions to judgments supposed to be universal, 
and in the consequently more exact determination of 
those judgments through further search into reality, 
that advance in knowledge generally consists. 

The foregoing discussion has brought out that the 
chief formal distinctions in categorical propositions 



96 



THE LOGICAL BASES OF EDUCATION ch. vi 



Quality and 
Quantity in 
Hypotheti- 
cal and 
Disjunctive 
Judgments. 



are those of Quality, between affirmative and negative, 
and of Quantity, between universal and particular. 
The latter distinction is determined by whether the 
proposition refers explicitly to all the individuals 
which bear the subject name, or whether its applica- 
tion is indefinite. 

§ 5. — If we now ask whether the same distinctions 
can be applied to hypothetical and disjunctive judg- 
ments we find that this is only very partially the case. 
The negative form is perfectly appropriate to the 
hypothetical judgment, for a condition M may be 
found united with S, which is incompatible with P, 
and this is appropriately expressed by the form " If S 
is M it is not P." It is also possible to write par- 
ticular judgments in a hypothetical form, and say 
" If S is M it may be P," and " If S is M it need 
not be P." But this does not make the judgments 
really hypothetical, and is, therefore, misleading. 
Every particular judgment directly asserts fact, and 
for this the categorical is the appropriate form ; 
whilst the special function of the hypothetical is to 
express necessary connexion of a result with its 
conditions. As such a connexion must be universal, 
the hypothetical form should only be used for 
universal judgments. 

Similarly, as the function of the disjunctive form is 
to express known relations within a system, it is evi- 
dent that a statement of the form "S may be P or Q" 
has little of the essence of disjunction in it : it is 
mainly an expression of ignorance, and the under- 
lying judgment is categorical. Further, it is impossi- 
ble to have a negative disjunctive judgment. If we 
would deny the disjunctive " S is P or Q " we must 
say " S is neither P nor Q," but this is not disjunctive 
but categorical. In short, the denial of a system does 
not involve the affirmation of an opposed system. 



CHAPTER YII 



FORMAL RELATIONS OF PROPOSITIONS 



§ 1. — We saw in the last chapter that the chief The Four 



formal distinctions of judgments are those of 
quality and quantity. It was by considering these, 
and ignoring the content of judgments, that the four- 
fold scheme of categorical propositions, which has 
been traditional in logic since Aristotle, was produced. 
For it is evident that a proposition must by its very 
form either definitely refer to the whole range of 
reality indicated by the subject or leave the scope 
of its application doubtful. The former case is ex- 
pressed in the affirmative by " Every S is P " or " All 
S's are P," the latter by " Some S's are P ; " in the 
negative the former by " No S is P," and the latter 
by " Some S's are not P." 

It should be noted that the form " Every S is not P" 
is not adapted to express the universal negative, 
because it is ambiguous. It may intend to deny P 
of every S which exists, when it is universal in its 
force ; or it may only intend to deny that we can 
affirm P of every S, and this would be true if P can 
be denied of a single S ; it is then particular. For 
instance if we affirm that " All that glitters is not 

H 



fold Scheme 
of Proposi- 
tions. 



DistrLbu- 
tion of 
Terms. 



98 THE LOGICAL BASES OF EDUCATION chap. 

gold," we do not mean that no glittering things are 
gold, but only that some glittering things are not 
gold. The proposition is, therefore, particular. 

It is possible to express more or less adequately 
every categorical judgment in one or other of these 
four forms, if we include the impersonal and demon- 
strative judgments under the particular ; and the 
judgments of particular relation and historical singu- 
lar judgments under the universal, on the ground 
that they definitely refer to the whole of their sub- 
jects. In doing so, however, we ignore the important 
distinction between such singular judgments and the 
true universals. Moreover, the form " Every S is P " 
is used indifferently for the mere results of counting, 
as " All the boys are tired," and the judgment of 
necessary connexion, such as " All equilateral triangles 
are equiangular." However, certain relations hold 
between these forms of proposition which we shall 
do well to examine briefly. 

The four forms of proposition are traditionally in- 
dicated by the letters A, I, E, O, which are the first 
two vowels in the Latin word aflrmo, I affirm, 
and the vowels in nego, I deny. The symbols are 
thus distributed— 

A Universal Affirmative... Every S is P. ^ 

I Particular „ ...Some S's are P. | 

E Universal Negative No S is P. 

O Particular „ Some S's are not P. 

§ 2. — We saw in chapter iii that every term has 
a meaning or content, and a denotation, or range of 
objects to which it is applicable. Both these aspects 
are always present in categorical judgments, but the 
denotation is the more prominent in the subject and 
the meaning or content in the predicate. As, how- 
ever, every term always has a reference to reality, it is 



VII FORMAL RELATIONS OF PROPOSITIONS 99 

permissible to consider the denotation of the predi- 
cate as well as that of the subject. A term is 
technically said to be distributed when definite refer- 
ence is made to the whole of its denotation. Thus 
the subjects of the A and E forms of proposition are 
distributed. When the predicates are examined, it 
is seen that those of the affirmative propositions are 
undistributed, for the assertion that P belongs to every 
S, or to some S's, evidently makes no definite refer- 
ence to the whole extent of the application of P ; other 
things besides the S's referred to in the proposition 
may be P. When we turn to the negative forms, 
however, we see that P is, in each case, distributed ; 
for whether it is every S or only some S's which are 
to be excluded from P, yet that exclusion is only 
made when they are shut out from every possible case 
of P, and P must therefore be explicitly referred to 
in its whole denotation. Summing up these results, 
we see that — 

E distributes both its terms. 
A „ its subject only. 

„ its predicate only. 

1 „ neither term. 



version. 



§ 3. — Dependent on this is what is called Con- Conversion. 

rsion, that is, the transposition of subject and pre- 
dicate in a proposition. In this process no undistri- 
buted term may be made distributed, for that would 
evidently be going beyond the assertion of the 
original proposition. 

It follows that E and I propositions can be con- 
verted simply ; that is, into propositions of the same 
form, as both the terms in each of these propositions 
are the same in distribution. Whether we say 
" No S is P " or " No P is S " ; " Some S's are P " or 
" Some P's are S," in each of the two cases we are 

H 'A 

L.OFC. 



100 THE LOGICAL BASES OF EDUCATION chap. 

expressing exactly the same idea, and the form in 
which we put it is a matter of no logical interest. 

It is also plain that an O proposition cannot be 
converted at all, for to pass from " Some S's are not P " 
to " Some P's are not S " would be to distribute 
S, and therefore to pass beyond the " Some S's " 
with which we start. 

If we now examine the A form of proposition, we 
see that it can only be converted to the I form, as 
the P is given us undistributed. This is appro- 
priately termed conversion by limitation. In this 
process, therefore, we pass from a more definite to a 
less definite assertion, for we lose sight of the 
distribution of S. From " All cats are animals " we 
reach by conversion " Some animals are cats ' ' which 
is only equivalent to " Some cats are animals." We 
have passed from expressing knowledge to expressing 
partial ignorance. As Dr. Bosanquet says, " We 
seem . . . only to have advanced to a doubt of what 
we knew."^ It is true that if we look at meaning 
there is a difference of emphasis in passing from, say, 
" All sponges are animals " to " Some animals are 
sponges." But this is of psychological rather than 
of logical interest; the judgment underlying both 
propositions is one single act of thought, and remains 
unchanged ; hence the new expre>ssion is inadequate. 

To call these processes of conversion, inference, is 
only justifiable if every change of form is held to 
indicate a change of thought, and this is certainly not 
the case. "The transposition is ... of rhetorical 
rather than logical value. ' Who deniges of it, Betsy ? ' 
inquired Mrs. Gamp; and then Mrs. Gamp, ]jy 
reversing the order of the question, imparted a more 
awful solemnity to it, ' Betsy, who deniges of it ?' 
This is the philosophy of all conversions and all 
1 Logic, vol. 1, p. 327. 



VII FORMAL RELATIONS OF PROPOSITIONS 101 



substitutions of one verbal equivalent for another, in 
a nutshell."! 

§ 4. — We have now to enquire how the truth or 
falsity of a proposition in any one of tliese four forms 
affects the truth or falsity of each of the other forms 
which deal with the same matter, that is, have the 
same subject and predicate. It has been traditional to 
call these relations of truth and falsity "the 
opposition of propositions," where the word " opposi- 
tion " merely means comparison of differences of 
form, whether those differences imply real opposition, 
i.e., incompatibility in meaning, or not. The re- 
lations have been for many centuries indicated in 
the following diagram, which is called " The Square 
of Opposition." 




S ub- contraries- 



Examining the propositions in pairs as indicated Suhaitcma 
by the diagram we take first the Subaltern relation, 
a name derived from the diagram. I and O are 

^ Hobhouse, The Theory of Knowledge, pp. 259—260. 



102 THE LOGICAL BASES OF EDUCATION chap. 

called " subalterns " to A and £! respectively, 
because they are written under those letters in the 
diagram. We see at once that the assertion of a 
universal obviously includes the assertion of its 
subaltern, i.e., the particular of the same quality. 
Thus, to assert A is to assert I ; to assert £ is to 
assert O. But this will not hold in the case of 
denial. The fact that the hasty psalmist was 
unjustified in affirming that " All men are liars " by 
no means proves that the more modest assertion 
" Some men are liars " would not be true. On the 
other hand this latter proposition will not justify the 
former : we cannot affirm the universal on the basis 
of the particular. But if we deny the indefinite 
particular, our denial evidently applies yet more 
strongly to its corresponding universal. 

When we take propositions of opposite quality we 
see that A and O, E and I, respectively, are pairs of 
Contradictories. The essence of contradiction is 
that of two contradictory propositions one must 
always be true and the other false. Thus to assert A 
is implicitly to deny O, to deny A is implicitly to 
assert O ; whilst these relations also hold the other 
way, that is, to deny O is to assert A, and to assert O 
is to deny A. Similar relations hold between ES and 
I. This all follows directly from the Principles of 
Contradiction and Excluded Middle. 

If the propositions considered are A and £1 then 
it is obvious that both cannot be true, but both may 
be false. That " No men are liars " would be as 
rash a statement as that "All men are liars." 
These propositions are called Contraries because the 
assertions made by them are the furthest removed 
from each other which it is possible to make about 
any one subject matter. 

Lastly, when we consider the two particular forms 



VII FORMAL Delations of propositions lo:; 

of proposition, I and O, we see that they are sub-con- 
formally indifferent to each other : both may be true '^""^ ^* 
together, and this is always the case when the 
' some ' is in fact limited to part of the denotation 
of S : that " Some men are liars " and that " Some 
men are not liars " are equally true. It is evident, 
however, that both these propositions cannot be 
false if there exist any S's at all ; this directly 
follows from the Principle of Excluded Middle. 
These propositions are technically called Sub-con- 
traries, simply because of their position in the 
diagram of the Square of Opposition. 

If we now collect our results we see that when 
A is true, the truth of I and the falsity of both E 
and O are implied ; but when A is false the only 
implication is the truth of O. Corresponding results 
hold with E. 

Again, when O is false, the falsity of E and the 
truth of A and I are implied ; but when O is true, 
nothing is implied but the falsity of A. Similar 
implications are involved in the truth or falsity of 
I. 

To put it generally : the truth of a universal, or 
the falsity of a particular carries with it implications 
as to the truth or falsity of each of the other 
members of the four-fold scheme ; but the falsity of 
a universal or the truth of a particular only implies 
the truth or falsity respectively of its contradictory. 



CHAPTER VIII 

THE METHOD OF KNOWLEDGE 

Truth and § 1.— In chapters V and vi we considered what 
^ ^'''^®- is implied by the act of judgment at its various 
stages of developnient, and so found an answer to 
the fundamental question as to the meaning or 
content of judgment. There remain for examination 
the two much more difficult enquiries relating to 
truth^nd evidence, and these will occupy us through- 
out the remainder of the book. These two questions 
cannot well be separated. No one ever accepts as 
true a statement which does not rest on evidence which 
he deems sufficient. But evidence which appears 
conclusive to one mind is often rejected by another 
as insufficient or even as altogether worthless. Our 
task, then, is to consider what is the final test of 
truth, to examine the kind of evidence on which 
judgments which satisfy that test are grounded, and 
to ascertain how such evidence is procured. In 
brief, we have to seek an answer to the question : 
By what method does man attain knowledge 1 

^ature of § 2. — Method implies orderly procedure, that is, 

^ "^ • procedure guided by some definite principle. It is 

only when a task is pursued methodically that it is 



CH. VIII THE METHOD OF KNOWLEDGE 



105 



well done, and the more difficult the task the greater 
is the need of method. To nothing does this apply- 
so forcibly as to that most difficult of all tasks — the 
acquisition of knowledge. Without method a 
desultory collection of pieces of information may be 
picked up, but nothing that deserves the name of 
knowledge can be attained. The nearer the method 
in any science approaches perfection, the greater are 
the advances made in that branch of knowledge. 
This has always been recognized by thinkers, and it 
may be said that all systems of logic have been 
simply attempts to formulate the essential features 
of the methods by which knowledge has been sought 
at various times. Thus the logic "current at any 
time is relative to the test of truth or knowledge 
accepted at that time. 

§ 3. — Logic, as an organized body of doctrine, 
originated with the> attempt of Aristotle to systema- 
tize the methods by which men's thoughts and beliefs 
could be brought into harmony with each other, and 
so fulfil the test of truth accepted by Greek thinkers. 

In the Middle Ages this test of truth was ex- 
changed for mere agreement with dogmas. Certain 
general propositions were accepted as self-evident, 
and the whole work of thought was to deduce the 
consequences of these principles. The mediaeval 
logic was an attempt to set forth in detail all the 
conditions under which such deductions could be 
made. It was extremely acute, but was naturally 
concerned with the bare form of thought, for truth 
was held to consist merely in agreement with certain 
original propositions whose truth was unquestionably 
accepted. This logic was derived from that of 
Aristotle, but practically omitted all those parts of 
Aristotle's work which dealt with the establish- 
ment of true universal propositions. Another con- 



Develop- 
meiit of 
Doctrine of 
Method — 
Aristotle. 



Mediceval 
Logic. 



i06 THE LOGICAL BASES OF EDUCATION chap. 

sequence of the mediaeval view of knowledge was a 
false conception of the function of logic. It was 
held that the province of logic was to legislate for 
thought ; to lay down the methods by which alone 
truth could be attained. 
Bacon, With the development of natural and physical 
science which began in the sixteenth century the 
mediaeval test of truth was gradually discarded, and 
the view arose that the only test of truth is agree- 
ment with fact. Such agreement could be neither 
proved nor disproved by the mediaeval logic, and so 
the need for a new formulation of the method of 
knowledge was felt. This task was avowedly under- 
taken by Francis Bacon. Unfortunately, however, he 
retained the mediaeval view that the function of 
logic is to lay down with authority the methods 
which scientific investigation must follow. He 
himself had not studied the methods by which 
Copernicus, Galileo, and the other great pioneers of 
science, really worked. He believed that an 
enormous collection of facts, followed by careful 
comparison and classification, would make the hidden 
truths of nature immediately obvious. The method 
was fundamentally a mistaken one, and, as Jevons 
says, " it has not been followed by any of the great 
masters of science."^ But it had the merit of drawing 
attention to the need of verifying theories by appeal 
to fact. " Against this . . . must be set the fact that 
by calling his method induction, and laying so much 
stress on the collection of facts, he fostered, and, 
indeed, fixed in the public mind the erroneous idea 
that the whole work of science consists in observa- 
tion."^ This idea really makes method mechanical; 
for it conceives method as an artificial arrangement in 

^ Principles of Science, p. 507. 

2 Minto, Logic, Inductive and Deductive, p. 253. 



VIII THE METHOD OF KNOWLEDGE 107 

a body of knowledge which is external to the mind 
and independent of its activity. This was indeed 
plainly claimed by Bacon himself : " Our method 
... of discovering the sciences is one which leaves 
not much to acumen and strength of wit, but nearly 
levels all wits and intellects." ^ 

Bacon's idea of method, as we have said, had little Neioton. 
influence on the actual work of scientific discoverers, 
and it is not to him but to Newton that modern 
science owes the first clear formulation of its general 
method. 

Logicians, however, long ignored the revolution mul 
which was being effected in the method of know- 
ledge, and continued to expound the old mediaeval 
logic, with all its claims to set forth the " art of 
thinking." This led naturally to logic itself falling 
into very general contempt ; its system was seen 
to be largely artificial, and out of relation to 
the modes of thought actually proved successful 
in every branch of science. To Mill belongs 
the credit of rescuing logic from death by inani- 
tion. He grasped the truth that the function of 
logic is not to dictate method to science, but to 
accept the methods which science finds successful in 
the ascertainment of truth, and by analysis to make 
clear their essential general features. Then, he hoped, 
the same methods which had led to such advances 
in the natural and physical sciences, might be found 
equally fruitful in those sciences which deal with the 
mental and moral life of humanity, such as history, 
sociology, ethics, and psychology. This view of 
logic has become the accepted one ; logic no longer 
claims to be the lawgiver to the sciences, but owns 
itself dependent upon them in its formulation of 
method. 

1 Novum Organum, I, 61. 



108 THE LOGICAL BASES OF EDUCATION cha?. 

Since Mill's great work, the development of logic 
has been chiefly in deepening and making more exact 
the conception of knowledge. It is seen that agree- 
ment wdth fact is not a sufficient test of truth, if 
' fact ' is restricted to mean something observed by the 
senses. Science more and more finds truth in uni- 
versal relations and laws, of which particular facts 
are but manifestations and examples. Our test of 
truth is that ultimate consistency and relation of 
universal judgments, verified by appeal to facts, 
which we mean by system. Thus the modern view 
is in one sense a return to that of Aristotle, but 
a return which lays emphasis also on that need of 
agreement with fact on which modern science rightly 
insists. 

§ 4. — This criterion of truth implies that method 
is essentially an order of thought, and not an order 
of things. It is that process of self-activity in which 
the mind of man satisfies its own rational nature by 
finding reason as the guiding principle of the uni- 
verse. It is not a process by which an order of 
external nature is stamped on a passively receptive 
mind. As Coleridge put it, " Method implies a pro- 
gressive transition, and it is the meaning of the word 
in the original language. . . . The term, method, 
cannot, therefore, otherwise than by abuse, be applied 
to a mere dead arrangement, containing in itself no 
principle of progression."^ It is the presence of such a 
principle of progressi(*n — of gradual development 
from incompleteness and imperfection towards com- 
pleteness and perfection of knowledge — which marks 
every true science. For a science is the result of 
mental activity bringing itself into harmony with 
world activity ; its success is marked by agreement 
with fact on the one hand, and by a growing appre- 
1 The Friend^ vol. iii, p. 116. 



viii THE METHOD OF KNOWLEDGE 109 

elation of the ultimately rational character of the 
grounds of knowledge on the other. 

§ 5. — Important, therefore, as it is to remember 
that knowledge is mental construction, it is equally- 
essential to bear in mind that it is construction based 
on sense experience, and subject throughout to the test 
of such experience. A method of knowledge must, 
therefore, analyse the ways in which this experience 
can be made explicit; in other words, enquire how an 
exact and definite knowledge of facts can be obtained. 
Now all human knowledge of material facts is derived 
in the last resort from direct observation. We 
shall have, then, to consider how we can guard 
against errors due to faulty or careless obser- 
vation, so that our fabric of knowledge may be 
based on a sure foundation. In a word we shall 
have to enquire how it is possible to obey the maxim 
'* jVlake sure of your facts." 

But though in the last resort all knowledge of 
facts rests on direct observation, yet that last resort 
is unattainable for every one of us in an indefinitely 
large number of cases. Every searcher after know- 
ledge has to accept much on the testimony of others. 
" In the best scientific work, even as in the worst, 
much must be taken upon trust ; on the authority of 
the competent observer, skilled instrument maker, or 
original investigator." ^ A method of knowledge must, 
therefore, indicate what tests of truth can be applied 
to testimony, so that only the trustworthy may be 
accepted. No formulation of method can be satis- 
factory which drops out of sight '* the complex inter- 
change of opinion, observations, experimental results, 
criticisms — the division of labour — that constitutes 
the life of science." ^ 

1 Ravenshear, Article on Testimony and Authority, Mind, 
N. S., vol. vii, p. 63, 2 jj^id, p. 64. 



110 THE LOGICAL BASES OF EDUCATION chap. 

§ 6. — The ascertainment of facts is, however, only 
the starting-point of knowledge. The very aim of 
every science is to extend knowledge beyond mere 
facts to those universal relations which can be found 
in those facts by the operations of thought, and 
to reason from those laws to their consequences, 
thus reaching knowledge of other facts which have 
not been observed, and binding the whole into one 
comprehensive system of knowledge. All such 
operations of thought are included under the general 
name of Inference. The aim of inference and the 
final step of method is thus seen to be the construc- 
tion of system and the finding in system that 
explanation which is the ultimate goal of thought. 

Our examination of Method will, therefore, fall 
under three main heads : — Observation and 
Testimony ; Inference ; System and Explanation. 
But these must not be regarded as three stages of 
progress separated in time. They are inseparable in 
the actual development and construction of know- 
ledge, though for convenience and clearness we can 
consider them apart. 

We have seen that system is simply the completion 
of inference, and it is obvious that the testing of the 
trustworthiness of testimony must also be a process 
of inference. It is not so evident at first sight that 
observation also implies inference, but further con- 
sideration shows that it is so. This will be worked 
out in our discussion of observation.^ It is sufficient 
here to point out that wherever error is possible we 
shall do well to suspect the presence of inference. 
The impression on the senses is what it is, but even 
in the simplest cases it may appear to us to be some- 
thing else, and so the judgment which expresses what 
the sense-impression is to us — i.e., what observation 
^ See Chapter xi. 



VIII THE METHOD OF KNOWLEDGE 111 

we have actually made — may be false.^ Now, the 
grounds of this falsity cannot be found in the mere 
sense-impression, for that asserts nothing. It must, 
therefore, be sought in the act of mental construction 
by which we bring that impression under a certain 
idea. And such construction is of the nature of 
inference, for it asserts the character of an impression 
on the grounds of its resemblance to impressions not 
now experienced. For example, the rustic who takes 
a gravestone brightened by the moon for a ghost, in- 
fers the ghost from the similarity of the sense-im- 
pression he actually receives with the brightness and 
whiteness which form the essential features of his 
idea of the appearance of ghosts, his inference being 
supported by the fact that the midnight hour is the 
orthodox time for ghostly manifestations. 

It appears, then, that the method of knowledge is 
inference throughout, and it will be necessary to 
consider the nature of inference before entering on 
an examination of the precautions which should be 
taken to secure that observation is expressed in true 
judgments of fact. 

§ 7. — Before taking up this enquiry, however, it Character- 
will be well to consider more definitely what is Metiiodicai 
implied in speaking of any process of thought as ^^o^g^^t. 
methodical. 

Such a process may combine an indefinite number Pmyose. 
of inferences ; it may be of any length and of any 
degree of complexity. But whatever its length or 
complexity, it is methodical just in so far as it is 
dominated by a purpose. All methodical thought, 
as we have seen, leads to system, and the idea of 
system is implicit in it from the first. Of course, in 
the beginning of an enquiry we have no system 
ready made. The actual concrete system which our 
1 Cf. pp. 22, 92. 



112 



THE LOGICAL BASES OF EDUCATION chap. 



enquiry aims at reaching is learned from the facts 
themselves. 

Observation of facts, then, suggests the kind of 
problems whose solution will constitute the system 
in which they have their place. So "in every 
science the next step after observing the facts is to 
formulate a series of questions according to some 
methodical system ; every science is composed of the 
answers to such a series of questions." ^ Often, 
indeed, an answer is suggested together with the 
question, and then this has to be tested. The 
process of finding or of testing the answers to the 
questions thus suggested will generally involve much 
more observation of facts, and this again will 
suggest other problems, and so one enquiry grows 
out of another. But unless the original observations 
are accurately made, the whole enquiry is likely to 
prove futile. Or again, if in any enquiry we start 
from a general proposition whose truth we assume, 
and that proposition is in reality wholly or partially 
false, then our labour is vain. 

These considerations yield us two closely related 
and fundamental rules of method — 

1. Have a definite purpose. 

2. Make sure of your starting-p)oint. 

§ 8. — Neglect of one or both of these leads to 
Fallacy, that is, to invalid thought disguised as valid 
thought. This is most likely to occur in exposition 



If the purpose is confused with the starting-point, 
we have the fallacy of Begging the Question, or, in 
its technical Latin name, Petitio Princiini. This 
means the assumption, as the basis of proof, of the 
very proposition we set out to prove, or of a proposi- 

^ Langlois and Seignobos, Introduction to tJie Study o, 
■History, Eng. trans, by Berry, p. 214. 



VIII THE METHOD OF KNOWLEDGE 113 

tion implying it. The possibility of expressing the 
same judgment in various forms of words renders it 
easy for such fallacious arguments to pass current. 
The fallacy is committed, for instance, when we are 
told that "opium produces sleep because it has a 
soporific quality," or that " the volume of a body 
diminishes when it is cooled, because the molecules 
then become closer." 

Perhaps the most common mode of committing this 
fallacy is the acceptance of sham axioms, generally 
received from tradition, and the use of them as bases 
for inference. Of these many thousands have been 
received amongst men, and many are still held with 
unquestioning faith. We will quote a few : That 
nature abhors a vacuum ; That other metals can be 
transmuted into gold ; That all men are equal ; That 
slavery is natural ; That all children are born wholly 
good ; That all children are born wholly inclined to 
evil ; That in all trading the gain of the one party 
is the loss of the other ; That dreams are prophetic j 
That like cures like. 

An excellent example of this form of the fallacy 
is to be found in the First Chapter of Mr. Herbert 
Spencer's EduGatio7i. After stating that " acquirement 
of every kind has two values — value as knowledge and 
value as discipline^'" the author discusses the value of 
most subjects from the point of view of knowledge. 
He then turns to disciplinary value and begins his 
remarks with the following 2^etitio : — " Having found 
what is best for the one end, we have by implication 
found what is best for the other. We may be quite 
sure that the acquirement of those classes . of facts 
which are most useful for regulating conduct, involves 
a mental exercise best fitted for strengthening the 
faculties. It would be utterly contrary to the beau- 
tiful economy of Nature, if one kind of culture were 



Iqnoratio 
Elenchi. 



114 THE LOGICAL BASES OF EDUCATION chap. 

needed for the gaining of information and another 
kind were needed as a mental gymnastic." ^ 

A vague conception of the purpose often leads to 
the fallacy of Arguing beside the mark — Ignoratio 
Elenchi as it is technically termed. To meet a man's 
arguments by a charge of inconsistency, or by personal 
abuse, is to furnish a case in point. " To knock a 
man down when he differs from you in opinion may 
prove your strength, but hardly your logic." ^ 

Another mode of committing the fallacy is to appeal 
to prejudice or to sentiment. The following " argu- 
ment " against the study of literature is a striking 
instance : " When a mother is mourning over a 
first-born that has sunk under the sequelae of scarlet- 
fever — when perhaps a candid medical man has 
confirmed her suspicion that her child would have 
recovered had not its system been enfeebled by over- 
study — when she is prostrate under the pangs of com- 
bined grief and remorse ; it is but small consolation 
that she can read Dante in the original." ^ 

The fallacy may also be committed by ignoring the 
arguments by which your opponent supports his con- 
clusion, and setting up in their place a " man of 
straw " which you then triumphantly demolish. A 
good instance is furnished by the objection to a 
classical education that " throughout his after career, 
a boy, in nine cases out of ten, applies his Latin and 
Greek to no practical purposes." * Or again : " As the 
Orinoco Indian puts on paint before leaving his hut, 
not with a view to any direct benefit, but because he 
would be ashamed to be seen without it ; so, 
a boy's drilling in Latin and Greek is insisted on, 
not because of their intrinsic value, but that he may 
not be disgraced by being found ignorant of them — 

1 Education, p. 41. ^ Stock, Deductive Logic, p. 313. 

3 Spencer, Education, p. 28. ^ Fbid, p. 2. 



VIII THE METHOD OF KNOWLEDGE 115 

that he may have ' the education of a gentleman ' — 
the badge marking a certain social position, and 
bringing a consequent respect." ^ Of course Mr. 
Spencer has no difficulty in showing that these are 
not valid grounds on which to select a curriculum. 
But such showing is the veriest beating of the air so 
far as the arguments based on the disciplinary value 
of classical studies are concerned. And it is on these 
that the advocates of such studies mainly rely. 

In using illustrations, we need to be continually 
on our guard against this fallacy. An illustration is 
intended to make clear something which the learner 
finds obscure. But the teacher may mistake the 
difficulty, and so direct the illustration to the wrong 
point. The same error may be made by the learner. 
For, as De Morgan well says, " the greatest 
difficulty in the way of learners is not knowing 
exactly in what their difficulty consists ; and they are 
apt to think that when something is made clear, it 
must be the something."^ Especially is this the case 
when an abstract relation is illustrated by concrete 
examples. There is always the danger that it is 
something in the particular examples really irrelevant 
to the point under consideration which has been 
understood, and generally " the minds which are best 
satisfied by material instances are also those which 
give themselves no further trouble." ^ 

Another form of this fallacy to which the use of 
illustrations is liable is that the learner may fail to 
see the analogy between the illustration and the 
difficulty it is meant to make clear. Such con- 
siderations show that great care is needed to make 
sure that an illustration really fulfils its intended 
function. 

1 Spencer, Education, p. 2, " Formal Logic, p. 266. 

3 Ibid, p. 267. 

I % 



116 



THE LOGICAL BASES OF EDUCATION chap. 



Essence of 
Methodical 
Process. 



Nature of 
Inference. 



§ 9. — Methodical process must, then, have a 
definite starting-point and a definite purpose. But 
it is in the continuous transition from the former to 
the latter, that method is found. We cannot have 
orderly procedure unless we first know whence we 
are starting and whither we wish to go. But it is 
quite possible to know these and yet to wander by the 
way. How such wandering may be avoided in any 
particular case must be determined by the special 
science concerned. Our task is only to find by the 
analysis of successful procedure, what are the general 
characteristics of such method. These character- 
istics may be summed up by saying that methodical 
process omits nothing, takes up the p)oints one hy one, 
and takes them up in such an order that it goes from the 
starting-point to the fidfilment of the purpose hy con- 
secutive steps, each of which is seen in its true relation 
to every other step and to the enquiry as a whole. 

§ 10. — It is evident that in the process of 
discovery nothing more than an approximation 
to this ideal can be expected, just because the 
system is in the process of making. It is only when 
the process is complete and has become proof that 
all which really lies outside the direct path can be 
swept away, and the passage of thought from 
starting-point to goal be seen as a necessary and 
continuous transition. Such perfect examples are, 
for instance, found in many of Euclid's proofs of 
geometrical truths. A process of inference is, then, 
logically perfect when it has ceased to be discovery 
and has become proof. Whether the process is 
familiar or new to any individual mind has nothing 
to do with its logical character. It is, therefore, a 
mistake to confine the term ' inference ' to cases in 
which an individual reaches a truth hitherto un- 
^iiown to him. The essence of inference is that 



VIII THE METHOD OP KNOWLEDGE 117 

thought passes continuously from starting-point to 
conclusion in a path necessitated by the character of 
the system. The conclusion is ' new,' not in the 
sense of being unfamiliar to any particular person, 
but in the sense of not being apparent in the 
premises — or judgments from which the process 
starts — though it is a necessary consequence of their 
combination. The inference is the whole construction, 
not the mere passage of thought between beginning 
and end. 

The question of inference then is this : Given inference 
certain truths, how can we reach other truths which ^^^ System. 
go beyond those which are given '? The answer 
must be sought in the conception of system with 
which inference is indissolubly connected. When- 
ever we can put a given fact or a given judg- 
ment into a sj^stem, we are able to make it the 
starting-point of inference. For instance, suppose 
we have a small bud from a rose-tree. What 
is apparent to observation is just a little green 
hard object about the size of a pea. If we pull it 
to pieces we can observe more, but we cannot 
observe in that rose-bud the full flower which would, 
under favourable conditions, have developed from it 
if it had been left on the tree. But when we see a 
rose-bud we are able, not simply to think about the 
rose-bud as it is now, but to carry our thoughts on 
to the full-blown rose. This is possible because we 
have sufficient knowledge of the matter to know 
that bud and flower are parts of the one system 
of the life of the rose-tree, so related that flower 
is the natural outcome of bud. We are then 
able to construct that system in our minds, and 
from that construction to derive the judgment 
that the flower should follow the bud. Evidently 
the definiteness of our conclusion is dependent 



118 THE LOGICAL BASES OF EDUCATION chai'. 



the extent of our knowledge of rose-tree 
One person may be able to state only the 
general fact of sequence, another will give more or 

will 



upon 
life. 



less approximately the time 
occupy. The more exact the 



the transition 
mental construction, 
the more exact is the conclusion which that con- 
struction makes apparent. 

We borrow the next example : "My train is half 
an hour late. I know I must miss my connexions 
at the station ahead ; for the train I am hoping to 
catch at that place is scheduled to leave five minutes 
after the time of arrival of the train I am now on. 
The time relations here necessitate my missing my 
connexions. This is rendered still more certain if 
they are rival roads ; on no account will one wait 
for the other. Moreover, the train I hope to make 
is made up and leaves the station in question, and 
so I cannot fall back upon the favouring chance 
that it also may be detained en route, and so enable 
me, after all, to reach it in time. Thus, with every 
additional knowledge of the system which forms the 
ground of my inference, and the various conditions 
which affect it, the validity of my inference is 
thereby increased." ^ 

Inference is, then, mental construction based on 
knowledge of particular systems and of such a 
character that a result not explicitly given in the 
premises can be immediately apprehended by thought 
when the construction is made. It is obvious from 
this that our power of inference is in every case 
essentially relative to the amount of our knowledge 
of the appropriate system. For example, a little 
child or a savage sees a heap of gunpowder for the 
first time, so that to him it is merely a heap of some- 
thing like black sand. The civilized adult who 
^ Hibbeii, Inductive Logic, p. 10. 



vm THE METHOD OP KNOWLEDGE 119 

recognizes it as gunpowder puts it into a different 
system, which embraces and goes beyond that of the 
child. From this system he can infer the effects of 
the apphcation of a lighted match — a result which the 
child or savage could only discover by an experiment 
which might be disastrous. But the gunpowder is 
the same, whether observed by child or gunner or 
chemist ; the difference is in the system of knowledge 
possessed by the observer. It is this which makes 
inference possible, though it is not itself inference. 

When we know a system we can pass from fact to inference 
fact within it. But the path from fact to fact is versais. 
always through a universal relation, that is, through 
some identical quality common to both the facts. 
All increase of knowledge is the finding such univer- 
sals. The more universal ideas we can think a thing 
under, the more we know about it, and every such 
idea is a relation. Inference cannot stir without 
universals, but it must be remembered that the 
universals are in the facts, only needing to be found 
there by thought, though they cannot be discerned 
by the senses. 

Inference, then, is the working out of system — the 
thinking facts under universal relations, and the 
finding universal relations exemplified in facts. A 
mere fact which cannot be brought into any system 
is meaningless to us ; and the greater the number of 
systems a fact can be placed in the more it means 
to us. Incidentally it may be pointed out here that 
the aim of teaching is not to impart facts but to 
develop systems ; facts are only of value in so far as 
they are starting-points for such development. 

§ 11. — Inference, or the making explicit the con- Deductive 
tents of a system, is a process which may begin from, ductive 
either of two starting-points. We may know some inference. 
universal relation which covers the whole system. 



120 THE LOGICAL BASES OF EDUCATION chai*. 

and from that proceed to develop by inference the 
particular contents of that system. This method of 
inference is called Deductive. It starts with the 
universal and applies that universal to the particulars 
which express it. It is, therefore, predominantly a 
synthetic process, as its function is to bind together 
particulars in a known system. 

On the other hand we may have only a number of 
given facts, and our task is then to find a system 
which will exhibit all these facts in consistent 
relations to each other and to the rest of human 
knowledge. This is called Inductive Inference. It 
starts with particulars and tries to find the 
universal they embody. Thus it is primarily an 
analytic process, as it can only find the universal it 
seeks by analysing the given facts. This makes it 
more or less tentative, as every particular fact 
embodies many universals, and more than one 
solution of an inductive problem is, therefore, likely 
to present itself. 

It follows, of course, that deduction is the easier 
process ; for^, given the premises, only one construction, 
and consequently only one solution, is possible. " In 
Induction you are finding out the system piecemeal, 
in Deduction you already have the clue ; but the 
system and the system only, is the ground of 
inference in both. Induction is tentative because 
we do not know the system completely," whilst " in 
deduction we are sure of having knowledge which 
covers the whole system." ^ 

Both deduction and induction, then, aim at making 
evident what a system involves. Looked at thus, 
they are seen to be two sides of one process, and not 
,two separate and opposed kinds of inference. Every 
system is built up on inductions, for our universals 
^ Bosanquet, Essentials of Logic, p. 162. 



Viii THE METHOD OF KNOWLEDGE 121 

are found by analysing experience ; deduction, 
therefore, implies induction. On the other hand, as 
we shall see later on, induction involves deduction ; ^ 
consequently, when we examine the processes in 
detail we shall begin with deduction. 

§ 12. — Induction and Deduction are, indeed, but Analysis 
expressions for those fundamental and mutually in- thesis. 
volved processes of analysis and synthesis which we 
have already found to be implicit in every judgment, 
that is, in every expression of knowledge or belief. 
We are now in a position to see more clearly what 
is meant by saying that each of these implies the 
other. Induction is primarily analytic, because it 
works by analysing or mentally separating the 
elements which compose a given fact. But it is also 
synthetic, " for we not only get internal connexions 
in our given material, but travelling beyond it, we 
take it as one member in a group of instances. 
Beginning with the individual case we are investi- 
gating, we go on to others of the self -same nature." ^ 
These others we bring under the universal law we 
have found, or, in other words, we include them in 
the system we are constructing. On the other hand, 
deduction is primarily synthetic, as it is ostensibly, 
this very process which we have just seen to be im- 
plicit in induction. But by following out the univer- 
sal relations of a system into its details, we are 
analysing that system unawares, and turning the 
vague idea of it with which we started into clear and 
definite knowledge. As Mr. Bradley admirably puts 
it : " Analysis is the synthesis of the whole which it 
divides, and synthesis the analysis of the whole which 
it constructs." ^ These two are, then, different sides 
of one process, the object of which is to show a system 

^ See ch. x. ^ Bradley, The Principles of Logic, p. 435. 
3 Ibid., p. 431. 



122 THE LOGICAL BASES OF EDUCATION ch. viil. 



as a clearly articulated whole. They differ in start- 
ing-point, in the end in view, and in the mental 
process of which we are conscious. But when the 
result is reached, it is always apparent that it has 
the two-fold character of exhibiting at once the 
unity of the whole and the differences of its parts. 
Advance in knowledge is, then, advance in both 
analysis and Synthesis. "The more deeply you 
analyse a given whole, the wider and larger you 
Qiake its unity ; and the more elements you join in 
a synthetic construction, so much greater is the detail 
and more full the differentiation of that totality."^ 

§ 13. — It follows from what we have said that 
whether the anatytic or the synthetic method is 
mainly adopted in any particular science depends 
upon the extent to which that science has been 
organized as a system. The more fully this has been 
done, the more deductive inference preponderates, for 
the more possible it is to start fresh enquiries from 
universal relations which have been previously 
established. On account of its very abstract nature 
and the simplicity of the axioms on which it is based, 
mathematics is the most deductive of the sciences, 
and the more any particular science is able to bring 
itself into touch with mathematics the more the 
synthetic method takes the place of the analytic 
method in that science. Physics and astronomy 
have in this way, become mainly synthetic in 
method. On the other hand, biology is still' largely 
analytic in its method, though the adoption of the 
great principle of evolution is gradually making it 
more synthetic. Geology and chemistry are still 
compelled to follow mainly the analytic method, 
whilst history, based as it must always be on 
testimony, can probably never do anything else. 
1 Bradley, The Principles of Logic, p. 447. 



CHAPTER IX 



DEDUCTIVE INFERENCE 



§ 1. — Deductive Inference is the establishment of Kinds of 
some particular relation by placing it in an appro- inference! 
priate system. Now this may be done with greater 
or less definiteness. We may be able to say no more 
than that we have a case which falls under a certain 
system, without being able to construct that system 
in detail. Then the inference is one of Suhsumption, 
which simply means that it sets forth a particular as 
an example of a universal. Such an inference is 
based upon the relation of subject and attribute, that 
is, upon the assertion that a certain concrete subject 
possesses a certain attribute, as " Wolves are 
savage," or "Slavery is derogatory to human nature." 
But of a concrete subject many such assertions are 
possible. It is because of this concrete cha- 
racter, that no single construction can give us the 
whole system, and it follows that in every subsump- 
tive inference it is necessary to state explicitly 
which of the universal relations involved in the 
system is made the basis of the inference. 

In other cases the relations involved are much 
more definite, because they are purely abstract. 



124 THE LOGICAL BASES OF EDUCATION chaf. 

Then the whole nature of the system stands revealed 
by the combination of the given elements, and it is 
not necessary to restate that nature in a more 
abstract form. In such cases the inference may 
be simply called one of Construction ; the best ex- 
amples of this are found in geometry and other 
branches of mathematics. We must consider these 
two forms of deductive inference separately. 

SYLLOGISM 

Nature of § 2. — Suhsumptive Inferences were fully analysed by 
y ogism. ^j.jg^Qt^lg^ g^^^ ^Y^Q results set forth in the doctrine of 
the Syllogism. Aristotle defined syllogism as "a 
form of reasoning in which certain facts being 
assumed, something else differing from these facts, 
results in virtue of them." Stated explicitly, a 
syllogism consists of three parts — (1) the Major 
Premise, which sets forth the universal relation on 
which the whole construction rests ; (2) the Minor 
Premise, which brings a particular case under the 
major ; (3) the Conclusion, ■ which sets forth the 
necessary consequence of this combination of 
premises. 
Distributed Now it is evident from this statement that the 
Term. premises must have an element of identity as a 

connecting link. This is embodied in the Middle 
Term, that is, the term which is common to both 
premises, and by means of which the minor is 
subsumed under the major. Symbolically then, we 
may state a syllogism thus — 

Major Premise M is P, 

Minor Premise S is M ; 

Conclusion • . S is P. 

IJhe first essential of syllogistic inference is, then, 



IX DEDUCTIVE INFERENCE 125 

that there should he an identical middle term con- 
necting the premises. This can only be formally 
secured by obeying the traditional rule that " the 
middle term must be used in its full extent in at 
least one of the premises," that is, that there must be a 
definite assertion about every M. If we have as 
premises " Some oranges (M) are sweet (P) " and 
" This (S) is an orange (M)," we can draw no certain 
conclusion as to the sweetness or otherwise of this 
particular fruit, though doubtless we shall think its 
sweetness more or less probable. Some amount of 
such weakness belongs to every major premise 
which is merely derived from experience and does 
not rest on a necessary connexion of attributes. 
" He is a fool,'' says Mrs. Poyser, " who can see the 
cat go into the dairy and ask what she has 
gone there for." Here, no doubt, experience is 
strengthened by a knowledge that cats like cream, 
but the conclusion that every time a cat enters a 
dairy its intentions are felonious is not a necessary 
one, though its probability is sufficiently strong to 
Justify immediate action on that conclusion. Thus 
it is evident that the strength of conviction with 
which we accept a conclusion is proportionate to the 
amount of probability we feel as to the M being 
really identical in our premises. 

The traditional doctrine of syllogism rejected all 
inferences which do not give a certain and definite 
conclusion. This was a natural thing to do when it 
was believed that ultimate truths of a self-evident 
character could be found in every department of 
knowledge. The nature of some of these * truths ' 
has already been indicated.^ We no longer believe 
in such a mechanical road to knowledge, and we are 
conscious that the majority of our conclusions, 
1 Of, p. 113. 



126 THE LOGICAL BASES OF EDUCATION chap. 

though probable enough for all practical purposes — 
that is, as guides to action of various kinds — are yet 
not supported by evidence so cogent as to make 
them absolutely certain. An investigation of the 
method of knowledge must, therefore, take account 
of inferences which only yield more or less probable 
conclusions. So long as we are careful to distinguish 
between conclusions which are certain and those 
which are only probable, no fallacy is committed. 

But it may be asked — Is the formal rule to refer 
explicitly to " every M " the only way of securing 
that M is identical in both premises ? To this the 
answer is that if the major really rests on a necessary 
connexion of attributes, the M can always be thus 
expressed. Science, as we have seen, aims at 
establishing reciprocal judgments.^ When such a 
judgment has been established it is a matter of 
indifference which term is made the grammatical 
subject and which the predicate of the proposition 
which expresses it. There are many such judgments 
in chemistry. For example, a liquid is tested by 
dipping into it a piece of blue litmus paper ; if the 
paper turns red, the conclusion is drawn that the 
liquid tested is an acid. The inference would 
probably be set forth in this form — 

All acids (P) turn blue litmus paper red (M), 

This liquid (S) turns blue litmus paper red (M) ; 

Therefore, this liquid (S) is an acid (P). 
Thus stated the syllogism is formally invalid 
because no explicit reference is made to " every M " 
in either premise. But as the major is a- reciprocal 
judgment, it may be equally well expressed in the 
form, " All liquids which turn blue litmus paper red 
are acids," and if this is put as the major premise the 
formal flaw disappears. Of course it is only because 
1 O/. p. 88. 



IX DEDUCTIVE INFERENCE 127 

the major is reciprocal that this change of form is 
allowable. We must conclude, then, that no 
syllogism is valid unless it can be stated in a valid 
form. 

The second essential of syllogistic inference is that 
the conclusion must not assert more than is warranted 
hy the p7'emisesj a requirement which syllogism shares 
with all other forms of inference. If, under the general 
major " Every M is P," we bring as minor " This S 
is M," or "Some S's are M," it is evident that we should 
only refer in the conclusion to just the very same 
S or S's. We can only draw a conclusion about 
" every S " when the minor premise definitely refers 
to every S. Or, to put it in another way, from a 
minor " S may be M," united with a major " M is P," 
we can only conclude that " S may be P." As 
there is no necessary connexion affirmed in the 
minor, none can be asserted in the conclusion. 

Similarly, the whole scope of P can only be referred 
to in the conclusion when it is definitely referred to 
in the major premise. Such explicit reference to the 
whole application of the predicate is only possible in 
a negative judgment, and there it is always made. 
Hence, to infer from the premises " All fishes (M) are 
cold-blooded (P) ; No whales (S) are fishes (M)," that 
"No whales (S) are cold-blooded (P)," is an invalid 
inference, though both premises and conclusion hap- 
pen to be true. And this draws our attention to an 
important point, namely, that the validity of a syllo- 
gism is not to be tested by the truth or falsity of 
its conclusion, but by whether the premises warrant 
that conclusion. A good position may be supported 
by very bad arguments, and in such cases the con- 
struction ofiered as its support is not the evidence 
on which its truth really rests. Of course, the 
question as to the truth of our premises is one of 



128 THE LOGICAL BASES OF EDUCATION chap. 

equal importance with the question as to the validity 
of our inference, but it is one which syllogism 
does not attempt to answer. The characteristic of 
syllogism is that it starts from premises assumed to 
be true ; the grounds for such assumption must 
usually be sought in induction. 

The requirement that the conclusion must not go 
beyond the premises in the scope of its assertion 
raises the question whether such a construction is a 
valid inference at all. It has been urged that if 
from the premises " Every M is P," " S is M," we 
draw the conclusion " S is P," we are guilty of the 
fallacy of petitio pri7ici2ni.^ Doubtless if our major 
premise rested on an exhaustive enumeration of in- 
stances, as its mere form suggests, we should not 
be justified in asserting it unless we had examined 
S among other instances of M, and so this charge 
would hold. But when we remember that the real 
justification of the major is a known necessary con- 
nexion of S and P, then the charge is seen to be 
itself a petitio, as it assumes the very point to be 
proved, viz., that the major is the result of a com- 
plete enumeration of instances of M. I may know 
that every candidate who gets less than x marks in 
mathematics fails in a certain examination, and this 
knowledge is quite independent of whether I am 
acquainted with the marks actually scored by an}^ 
of the candidates who do fail. The major is based 
on the regulations applicable to the examination, and 
is the real and true ground of the failure of all can- 
didates who fulfil the condition it lays down. 

Again, it has been urged that syllogism is not in- 
ference, because immediately we have the premises 
we have the conclusion. It may be replied that if 
this were not so it would not be inference, for the 
1 Cf. p. 112. 



IX DEDUCTIVE INFERENCE 129 

essence of all inference is that the premises necessi- 
tr.te the conclusion. This objection is based on two 
confusions. The first is that looking upon novelty 
as the essence of inference, which has been already 
dealt with.^ The other is the confusion between the 
judgments which form the premises as mere judg- 
ments, and as premises. As mere judgments — 
that is, as separate from each other^ — neither 
of them involves the conclusion. When they are 
combined as premises the conclusion is the necessary 
consequence not of the judgments but of their 
combination. 

The remaining rules of syllogism are self-evident Minor Rules 
and need not detain us. They are that one premise gism. 
TTiust be affirmative, and that an affirmative conclusion 
can only he the outcome of two affirmative premises. 
As a negative judgment explicitly denies a relation, 
it is evident that two such denials of relation to M 
can establish nothing. And equally evident is it 
that a denial in the premises must be represented by a 
corresponding denial in the conclusion, and vice versa. 

§ 3. — Aristotle considered in detail how many com- Forms of 
binations of premises would yield valid syllogisms, ^ ^gism. 
but the enquiry is mainly of antiquarian interest. Any 
construction which claims to be a S3dlogism can be 
tested by the four rules we have considered above. 

One other point only demands notice, and that is 
the distinction of Figure. Aristotle distinguished 
three figures according to the position of the middle 
term in the two premises — 

Fig. I. Fig. II. Fig. III. 

Major Premise M— P P—M M— P 

Minor Premise S— M S— M M— S 



Conclusion •. S— P . '. S— P . % S— P 



Cf. pp. 116-117. 



& 



130 THE LOGICAL BASES OF EDUCATION chap. 

Of these only the first is really an analysis of 
subsumptive inference, for it alone has a true major 
premise ; that is, a universal under which the minor 
is brought. In the other figures the premises are the 
same in kind, and this involves that they cannot 
oive a certain universal affirmative conclusion. Their 

o 

most important function in the method of knowledge 
is that they are steps in induction. We shall, there- 
fore, postpone further consideration of them to a 
later stage. ^ 

The mediaeval followers of Aristotle added a 
fourth figure showing the remaining possible arrange- 
ment of terms — 

Major Premise P — M 

Minor Premise M — S 

Conclusion •. S — P 

This is certainly a possible symbolic form, but it 
corresponds to nothing in the actual structure of 
thought, and should, therefore, be discarded. 
Hypo- § 4. — The universal judgment, as we have seen, 

Syllogisms, is often most exactly expressed in hypothetical form. 
We may, then, have syllogisms in which the minor 
premise brings a particular case under a universal 
relation of the form "If S is M it is P." Now 
from this mere form we must not assume that M is 
the only possible condition under which S is P, for in 
most of the judgments of ordinary life neither M nor 
P are stated with sufficient accuracy.^ We must, 
then, face the possibility that S may be P under other 
conditions, as X, Y, Z. For instance, " If a man (S) 
is shot through the heart (M) he dies (P)," but there 
are many other possible causes of death. It follows 
that we cannot infer " S is not P " from the 
conjunction of such a major premise with a minor of 
1 See Chaps, xi. and xiv. 2 qj-^ ^^ gg, 90. 



IX DEDUCTIVE INFERENCE 131 

the form " S is not M " ; for S may be X or Y or Z, 
and in either of these cases it is P. Again, 
the assertion "S is P" united as minor with the 
major " If S is M it is P " will not justify us in 
asserting " S is M," for P may in this case be due 
to X or Y or Z. We have then only two forms of 
syllogism with a hypothetical major premise which 
yield a certain conclusion. They are — 

(1) If S is M it is P, 
But S is M ; 
Therefore, S is P. 

(2) If S is M it is P, 
But S is not P ; 
Therefore, S is not M. 

To put it generally : a certain and definite conclusion 
can be drawn from either affirming the antecedent 
or denying the consequent of the hypothetical major 
premise. But to deduce such a conclusion from 
denying the antecedent would be to commit a formal 
fallacy analogous to the illicit extension of the 
reference of the major term in categorical syllogism. 
This is evident when it is seen that every hypo- 
thetical syllogism can be expressed categorically 
by writing the major premise in the form 
" Every S M is P." The minor " This S is not M " 
may be expressed : " This is not S M." If then 
these two propositions are combined 

Every S M is P, 
This is not S M ; 

it becomes evident that we are not justified in con- 
cluding " This is not P." 

K 2 



Nature of 



132 THE LOGICAL BASES OF EDUCATION chap. 

Similarly, if we affirm the consequent, the syllogism 
may be categorically expressed 

Every S M is P, 
This is P ; 

and it is seen that the middle term P is not dis- 
tributed and consequently we are not justified in 
affirming " This is S M." 

Hence, it is a matter of indifference, so far as the 
formal accuracy of our inference is concerned, 
whether we state it in a categorical or in a hypo- 
thetical syllogism. 

CONSTRUCTION 

§ 5. — We must now consider the characteristics of 
Construe Q instruction. In such inferences as '' A is north of 
B and B is north of C, therefore A is north of C," 
the conclusion follows obviously and immediately from 
the construction. But that construction is not 
syllogistic, for there is no middle term ; we have 
*' B " in one premise and " north of B," in the other. 
No doubt we can put the whole into syllogistic form 
by using as a major " What is north of anything is 
north of that which the former is north of." But 
this is merely the construction itself generalized and 
put in a more abstract form ; it is not the ground 
on which the inference actually rests. In such 
inferences, as in all others, we must have a point of 
connexion between the premises. But the mere 
presence of the same term in each is not enough ; that 
term must stand in the same kind of relation in 
each. As Mr. Bradley says, " ' A runs faster than B 
and B keeps a dog (C),' ' A is heavier than B and B 
precedes C,' ' A is worth more than B and B is on 



IX DEDUCTIVE INFERENCE 133 

the table (C),' or ' A is like B and B is like C/ 
You may doubtless extract some kind of inference 
out of these premises, but you can hardly go from 
them to any definite and immediate relation between 
A and C." 1 

Now, it is evident that the relations between things 
are indefinite in number, and consequently it is 
impossible to make a list of valid inferences. All 
that can be done is to consider the " tests of the 
general possibility of making a construction ; but of 
the actual construction there can be no canons." ^ 

§ 6. — The general principle of such constructive Types of 
inferences is that the construction exhibits the whole tion— 
contents of the system. They are of two main 
classes (1) those in which the constructed whole is a 
mere sum of its elements, the typical examples being 
arithmetical constructions ; (2) those in which the 
elements united are relations, the most typical 
examples being geometrical constructions. In each 
case the process can be immediately generalized ; 
for as the whole of the system is explicit in the con- 
struction, any precisely similar construction will 
yield a precise^ similar result. 

If we consider the iudfirments of arithmetic we find Arithmeti 

-, . ^ r, •, -vT • Construc- 

they are based on the idea oi a unit. JNow m uons. 
counting concrete objects " the mind always chooses 
its own unit ; it groups its objects as it pleases, and 
chooses as units the groups it has made : sometimes 
it counts by faggots, sometimes by single sticks." ^ 
The unit is, then, something determined not by the 
nature of things but only by the act of mind which 
discriminates things from each other. Objects alto- 
gether unlike in their qualities may be counted if we 
choose, just because they are alike in this one point, 

1 The Principles of Logic, p. 233. ^ Ibid., p. 246. 
3 Bryant, Educational Ends, pp. 192 — 193. 



134 THE LOGICAL BASES OF EDUCATION chap. 

that they can be discriminated from each other. 
Thus, a unit is a purely abstract individuality, and 
is at bottom nothing but an act of discrimina- 
tion. Counting may be aided by the presence of 
concrete objects, but it is independent of their 
nature ; its elements are the mental acts of 
discrimination. Hence, the constructed whole is 
purely abstract ; the elements and the whole are 
both made by the mind itself. 

Counting is the foundation of arithmetical judg- 
ments, and counting, beginning with one unit, is the 
gradual synthesis of units by adding one at a time, 
and giving a distinctive name to each new whole. 
But, as we have seen, all synthesis involves analysis, 
and the whole constructed is, by that construction, 
seen as the sum of its units. It is, of course, also 
apprehended as a whole of a certain definite 
character which distinguishes it from other wholes. 
It is because of these various characteristics that an 
arithmetical operation is an inference. " In these 
cases we are given certain elements, and assert that 
these elements ' form a certain whole. Both the 
elements and the whole must be such as to be known 
otherwise than in relation to each other, or we get 
into tautology. Thus, if 8 only meant 5 + 3 the 
statement 5 + 3 = 8 would be an idle play on 
words. But 8 also means 4 + 4, 10 — 2, 4x2, 
and I will venture to say that it also and primarily 
means 8."^ 

The primarily analytic operation with number is 
that of measuring, and this also rests on the conception 
of a unit. The object of measuring is to reduce 
what is given as a whole to a multiplicity of units, 
in order to compare it in respect of quantity with 
another whole similarly treated. Of course as a 
^ Hobhouse, The Theory of Knowledge, p. 424. 



IX DEDUCTIVE INFERENCE 135 

result the whole is apprehended as a synthesis of the 
units by which it is measured. It is unnecessary 
to pursue the subject further, our aim being only to 
make clear the character of the inference. 

Very few words need be added on constructions Geometrical 
of spatial relations. If we are given the definite uonV^'^' 
spatial relations — that is, the distance and direction — 
of both A and C to B, our construction, whether it 
remains purely mental or is aided by drawing a 
diagram, makes evident the spatial relation of A and 
C. All inference from charts and maps and plans 
is of this character. It is on constructions of this 
kind that the validity of geometrical axioms rests. 

§ 7. — As both arithmetical and geometrical con- inductive 
structions can be immediately generalized, they have 
an inductive aspect. Indeed, there is reason to *^°^' 
suppose that "mathematics in their primitive stages 
would have a quasi-inductive character. That is to 
say, that (1) they would tend to deal with concrete 
objects, or classes of such objects ; that (2) their 
results would have the aspect of independent 
generalizations, rules of thumb, and so on ; and that 
(3) they would be encumbered with difficulties in 
rising from these first generalizations to higher, 
more comprehensive, and more abstract principles. 
All these points seem to be borne out by the little 
that is known, or probably inferred, as to the early 
history of arithmetic and geometry." ^ The bearing of 
this on the method of teaching these subjects to 
children is obvious. 

^ Hobhouse, op. cif., p. 436. 



Aspect of 
Construe- 



CHAPTER X 



OUTLINE OF INDUCTIVE METHOD 



Meaning of § 1. — INDUCTIVE inference starts with particular 
tion.' facts and proceeds by a process of analysis to find 

the universal relations they embody, and so to 
construct a system whose nature explains them. 
The word ' Induction,' however, has been used, and, 
indeed, still is used, in more than one sense. 
Aristotle confined ' induction ' to generalization 
from sense-perception : " Induction begins with 
facts of personal experience and reasons backward to 
the cause or principle."-^ But such reasoning does 
not give really scientific knowledge, the appropriate 
expression of which is the syllogism. This is 
admirably put : " Nor is it possible to obtain 
scientific knowledge by way of sense-perception. 
For even if sense-perception reveals a cei'tain 
character in its object, yet we necessarily perceive 
this, here, and now. The universal, which is 
throughout all, it is impossible to perceive ; for it is 
not a this-now ; if it had been it would not have been 
universal, for what is always and everywhere we call 
universal. Since then demonstration (science) is 
1 Anal. Pr., II, 68, b., 32. 



CH. X OUTLINE OF INDUCTIVE METHOD 137 

universal, and such elements it is impossible to 
perceive by sense, it is plain that we cannot obtain 
scientific knowledge by way of sense." ^ 

It is just this establishment of universals which 
is the aim of modern science, and it is becoming 
more and more usual to apply the term ' induction ' 
to the whole process, instead of restricting it to that 
mere suggestion of a universal by sense-perception 
which corresponds to Aristotle's use of the term. 
'Induction' in this wide sense corresponds to the 
whole method of attaining knowledge, and includes 
deductive processes. 

§ 2. — Using the word in this wide sense, the General 
question is. How can the universal be found in the induction. 
particular 1 Not by sense-perception or observation, 
as Aristotle has so clearly shown in the passage 
quoted above. The universal can only be found by 
thought, that is, by supposing the existence of a 
certain law and then testing this supposition. As 
De Morgan tersely puts it : "A few facts have 
suggested an hypothesis, which means a supjjosition 
proper to explain them. The necessary results of 
this supposition are worked out, and then and not 
till then, other facts are examined to see if these 
ulterior results are found in nature." ^ The main 
steps of inductive method, may, therefore, be thus 
stated — 

1. A preliminary observation of facts. 

2. The formation of a hypothesis suggested by 
this observation. 

3. The testing of the hypothesis by comparison 
of its consequences with the results of a careful 
analysis of phenomena, with modification or even 

^ An. Post., 87, b., 28, quoted by Bosanquet, Ess. of 
Logic, p. 154. 

^ Budget of Paradoxes, p. 55. 



138 THE LOGICAL BASES OF EDUCATION chap. 

rejection if necessary. This process is carried on till 
the hypothesis is proved, when it is more correctly 
called a Law or Theory^ according to whether it states 
one universal relation or is a wider generalization 
covering many laws. 

It is in the third step that deduction is continually 
operative, for, as Dr. Bosanquet says, " nothing can 
be more deductive than the connexion of a hypothesis 
with the consequences by which it is verified." ^ 

§ 3. — The testing, moulding, and verification take 
a more direct, or a mainly indirect, form according to 
the nature of the case. When we are investigating 
a causal sequence in which the cause is simple and 
under control, we may try experiments with it, and 
our verification is a comparatively direct process. 
Even though the cause is not under our control, yet 
if the whole causal sequence can be observed under 
varying conditions, the process of testing and 
verification still remains partially direct. In this 
case, however, the more indirect method of de- 
ductively inferring the probable consequences of the 
cause and looking about to find if these consequences 
are really to be found in nature, will also be adopted. 
In all other cases this indirect method must be used 
nearly or altogether exclusively. " A cause . . . 
may be under control and yet be too dangerous to 
experiment with ; such as a proposed change of the 
constitution by legislation ; or even some minor Act 
of Parliament, for altering the Poor Law, or regu- 
lating the hours of labour. Here the first step must 
be deductive. We must ask what consequences are 
to be expected from the nature of the change (com- 
paring it with similar changes), and from the laws 
of the special circumstances in which it is to 
operate? And sometimes we may partially verify 
^ Logic^ vol. ii, p. 119. 



X OUTLINE OF INDUCTIVE METHOD 189 

our deduction by trying experiments upon a small 
scale or in a mild form." ^ 

When the facts with which we start are effects, 
and the causal sequence cannot be observed but 
must be inferred from those effects, as, for example, 
is mainly the case in geology, then the indirect 
method of verification is the only one available. 

^ Carveth Read, Logic, Deductive and Inductive, p. 164. 



CHAPTER XI 



OBSERVATION 



Importance 
of Observa- 
tion. 



knowledge starts 



Liability 
of Observa- 
tion to 
Error. 



§ 1. — The scientific method of 
with facts and continually returns to facts to test and 
verify its hypotheses. If its supposed facts are fictions, 
the whole fabric falls to the ground. It is a funda- 
mental question, therefore, how an accurate know- 
ledge of facts is to be obtained, and to this there is 
but one answer — by exact observation. Every state- 
ment of fact rests directly or indirectly on observa- 
tion. In the former case, the only question is as to 
the correctness of the observation ; in the latter case 
we must add to this an enquiry into the competence 
and trustworthiness of the witness who records it. 
In the present chapter we are concerned only with 
direct observation. 

§ 2. — At first sight it might seem that nothing 
need be said on this point. " Seeing is believing " 
is a proverb accepted by many as axiomatic. And, 
indeed, taken as expressing a common fact in the 
natural history of many minds, it is undeniably 
true. We are naturally apt to believe what we see, 
or rather, what we believe we see. But the mere 
fact of belief, as has been more than once insisted 



CH. XI OBSERVATION 141 

on, is no sufficient evidence of the truth of the judg- 
ment believed ; and what is commonly called " the 
testimony of the senses " is by no means infallibly 
accurate. Every case of illusion is an instance of 
this. As Aristotle long ago pointed out, a pea 
appears double when it is placed between two crossed 
fingers of one hand and then rolled about. Again, 
the two flat pictures in a stereoscope combine into 
an appearance of solidity. An immense number of 
other instances could be given. Further, the testi- 
mony of the senses is apt to contradict itself. " The 
moon at its rising and setting appears much larger 
than when high up in the sky. This is, however, a 
mere erroneous judgment; for when we come to 
measure its diameter, so far from finding our conclu- 
sion borne out by fact, we actually find it to measure 
materially less." ^ ISTor is such false testimony of the 
senses confined to individual experiences. "A vague 
and loose mode of looking at facts very easily observ- 
able, left men for a long time under the belief that 
a body, ten times as heavy as another, fails ten times 
as fast ; that objects immersed in water are always 
magnified, without regard to the form of the surface ; 
that the magnet exerts an irresistible force ; that 
crystal is always found associated with ice ; and the 
like." 2 

§ 3. — The possibility of such wide-spread errors Dependence 
as those of which Whewell here gives a few examples, tion on 
proves that men are generally bad observers, and, as In^owiedge. 
a consequence, that mere extended observation is no 
guarantee of truth. It is not how often an obser- 
vation has been made, but how accurately it has 
been made, that is the important point. And the 
accuracy which science demands is only possible 

^ Herschel, Discourse on Natural Philosophy, § 72. 
2 Whewell, Novum Organon Benovatum, p. 61. 



142 



THE LOGICAL BASES OF EDUCATION chap. 



when the observer possesses special skill and know- 
ledge. " A person may well derive, perhaps in some 
unfamiliar department of knowledge, a degree of 
certainty from the affirmation of the qualified expert 
far surpassing anything he could reasonably derive 
from his own imperfect or untrained observation." ^ 
Observation, in other words, is not a mere matter of 
perfect sense-organs, even when these are united 
with a concentrated attention and an earnest pur- 
pose to observe well. Only he observes well who 
brings much pertinent previous knowledge to the 
observation. " To make a perfect observer," says 
Herschel, " an extensive acquaintance is requisite, 
not only with the particular science to which his 
observations relate, but with every branch of know- 
ledge which may enable him to appreciate and neu- 
tralize the effect of extraneous disturbing causes." ^ 

§ 4. — This leads us to the very essence of the 
matter : observation always involves inference, and 
the correctness and value of every inference depends 
upon the truth and adequacy of its premises. For 
by ' observation ' we mean not the mere reception 
of sense-impressions, but the selection from amongst 
the whole mass of such impressions of those to which 
we will attend, and the interpretation of those 
attended to. And both selection and interpretation 
are matters of inference. 

When we select a phenomenon for observation we 
disregard a great deal more than we attend to, 
and we assume that this abstraction will not alter the 
character of what we are studying. But this assump- 
tion is a matter of inference and may be erroneous. 
In the seventeenth century Sir Kenelm Digby won 
much fame by the cures of wounds wrought by his 

^ Ravenshear, Article on Testimony and Authority, Mind, 
N. S., vol. vii, p. 65. 2 Op cit, § 127. 



XI OBSERVATION 143 

sympathetic powder. Says De Morgan: "The sympa- 
thetic powder was that which cured by anointing the 
weapon with its salve instead of the wound. I have long 
been convinced that it was efficacious. The directions 
were to keep the wound clean and cool, and to take 
care of diet, rubbing the salve on the knife or sword. 
If we remember the dreadful notions upon drugs 
which prevailed, both as to quantity and quality, we 
shall readily see that any way of not dressing the 
wound would have been useful."^ Similarly, "to-day, 
the Suffolk farmer keeps the sickle with which he 
has cut himself free from rust, so that the wound 
may not fester." ^ The error, as these examples show, 
may be either in excluding elements which ought to be 
included, or in including as essential those which are 
immaterial. This matter of selection is, indeed, one 
of the most difficult in scientific discovery, and we 
shall have to consider it in more detail in a later 
chapter.^ All we wish to make clear at this point 
is that whether an element should be included as 
important, or excluded as irrelevant, to the matter 
in hand is an inference from the knowledge which 
the observer brings to the observation. 

All interpretation is also inferential, for it Recogni- 
involves a reference to what is not now given 
in sense-perception. As an example let us consider 
the simplest possible case — that of recognition. We 
see a small yellow sphere of a certain size and we 
immediately recognize it as an orange. Doubtless, 
we are unconscious of any mental process, and so 
from the psychological point of view we might refuse 
to call it inference at all. But it has been already 
pointed out that the question for logic is the kind of 

^ Budget of Paradoxes, p. 66. 

2 Clodd, Tom Tit Tot, p. 64. 

3 Cf. Ch. xiv. 



144 THE LOGICAL BASES OF EDUCATION chap. 

evidence on which a judgment rests : if that is a 
mental construction from which a result necessarily 
follows we have inference. Now, the judgment 
" This is an orange " as an interpretation of the sight- 
perception we have spoken of, can only be justified 
by a construction such as the following — 

Oranges are spheres of a certain size and ap- 
pearance, 
This is a sphere of such size and appearance ; 
Therefore, this is an orange. 

Here the inferential character of the evidence on 
which our judgment rests appears plainly in the 
form of a syllogism in the second figure.^ But 
further, our conclusion carries much more with it 
than the visual qualities on which it is based. In 
calling the object perceived an ' orange ' we infer that 
it possesses many other qualities, as those of taste 
and smell and touch. And to this inference a very 
practical conclusion would be given by eating the 
orange. If we examine this second inference we 
shall find that it falls naturally into a syllogism in 
the first figure — 

Oranges are sweet, juicy, &c.. 

This is an orange ; 

Therefore, this is sweet, juicy, &c. 

Now, if these two syllogisms are examined it will 
be seen that both are formally invalid, in that in 
neither is the middle term used universally. The 
conclusions drawn should then not be stated as 
certain but as only probable — " This is probably an 
orange " ; " This may be (or is probably) sweet." 
But it will also be noticed that the conclusion in the 

1 Of. p. 129. 



XI OBSERVATION 145 

former case is much more likely to be true than that 
in the latter, because the signs by which the object 
is classed as an orange are of a definite character 
and have been directly observed. It is possible that 
a waxen or stone image might be made to resemble 
an orange so closely in visual appearance that it 
might deceive all but the most careful and minute 
observers. But the test of the other senses is an 
easy one to apply and is decisive. Such verification 
involves an inference in the first figure such as we 
have quoted above, and the comparison of its con- 
clusion with a new sense-impression. 

If, instead of the inferred qualities, attributes 
inconsistent with the recognition are found to be 
present as in the case of the stone image, then the 
recognition is rejected as unwarranted. This re- 
jection, like the original recognition, can be analysed 
into a syllogism in the second figure — 

No oranges are hard, gritty, &c., 
This is hard, gritty, (fee. ; 
Therefore, this is not an orange. 

Here the conclusion is certain, as the middle term is 
used universally in the negative premise, and so 
there is no such formal invalidity as in the former case. 

The inference in the first step of recognition is 
altogether implicit. Psychologically it is due to the 
habitual association of a certain group of attributes 
which we have learnt to sum up under the term 
' orange,' an association so perfectly mechanical that 
the presence of one or two of those attributes 
immediately suggests the w^hole group. But this 
suggestion is vague ; no one attribute is singled out, 
and the only thing in full consciousness besides what 
is given in sense-perception is the name. 

If we now turn to the second step we see that the 

L 



146 THE LOGICAL BASES OF EDUCATION chap. 

inference involved is somewhat nearer to being made 
explicit. From certain visual appearances we 
infer the presence of some definite non-visual 
quality or qualities, and we do so on the ground of 
their common inherence in the object we have recog- 
nized. There are, therefore, two chances that our 
conclusion is not true ; for the act of recognition 
may be unjustified, and, even if it is justified, our 
major premise may not be universal when we believe 
it to be so. The young child, for example, with ex- 
periences of only sweet oranges, would doubtless expect 
with the utmost confidence that any fresh example 
of orange would also be sweet ; the adult would know 
that this is open to considerable doubt, and would 
take for his major premise only the limited judg- 
ment " Some {or most) oranges are sweet." Now, 
when the child has his first experience of a sour 
orange, another conclusion is forced on him, and 
this also can find its justification in a syllogism, 
this time in the third figure — 

This is sour. 

But this is an orange ; 

Therefore ; oranges may be sour. 

Thus he proceeds to make his knowledge more 
exact and definite by forming sub-classes in his pre- 
viously wide and vague class ' oranges.' ^ 

The analysis which we have here applied to a very 
simple example holds true of every case of sense- 
perception. It shows that even in sense-perception 
we have all the essential features of the inductive 
method. The original recognition — liable to doubt, 
as we have seen it to be — is the hypothesis sug- 

1 This connexion of sense-perception with syllogism was 
first worked out by Dr. W. T. Harris ; see his Psychologic 
Foundations of Education, pp. 62 — 89. 



OBSERVATION 



147 



gested by a first observation of the facts ; then 
follows the inference of the results of that hypothe- 
sis, the testing of those results by further sense-ex- 
perience, and the consequent verification, modification, 
or rejection of the hypothesis. The most complex case 
of induction only contains the same steps, carried out, 
however, with infinitely greater difficulty and with 
infinitely greater liability to error, because the 
matter dealt with is infinitely more complex. 

Our analysis shows also that the possibility of error Distinction 
in observation is due to the inferential character of <oi3serva- 
the process, whilst the fact that the inference is ^j^^^ei^"*^^ 
largely unconscious renders it easy in cases of any ence.' 
considerable complexity for error long to escape 
detection. But our analysis has also made it plain 
that inference enters into the process in varying 
degrees ; there is less of it in the simple recognition 
than in the conclusion from that recognition that any 
particular quality, such as sweetness, will be found. 
Now it is evident that this second step may be 
developed to any extent, and may extend to conclu- 
sions which cannot be immediately tested by the 
senses. It is here that ordinary convention draws 
the line between ' observation ' and ' inference.' 
So long as we remember that observation itself 
involves inference, this distinction is a useful one. 
Suppose that, having recognized the orange, I drew 
the conclusion that it had been grown in Tangiers, 
that would obviously be an inference. Now, nothing 
would seem simpler than to distinguish between 
observation and inference in this sense of the terms. 
Yet nothing is more common than to confuse them. 
" Not one eye-witness in a hundred can adequately 
distinguish what he saw or heard from what he 
inferred." ^ The reason should now be evident. It 

1 Hobhouse, The Theory of Knowledge, p. 215. 

L 2 



148 THE LOGICAL BASES OF EDUCATION chap. 

is that psychologically such an inference as that the 
orange came from Tangiers, and such a judgment as 
" the orange is probably sweet," rest on evidence of the 
same sort, that is, evidence drawn from the previous 
knowledge of the observer. Logically, there is the 
difference that the latter deals with something which 
is directly given and so can be immediately tested by 
sense-experience, whilst the former asserts what is 
not so given and cannot be so tested. 

An illustration of our point may be drawn from 
Dr. Conan Doyle's ideal embodiment of the powers 
of precise observation and accurate inference, Mr. 
Sherlock Holmes. In the introduction to The 
Sign of Four his ingenuous biographer, Dr. Watson, 
writes — 

" ' You spoke just now of observation and deduction. 
Surely the one to some extent implies the other.' 

'Why, hardly,' he answered, leaning back luxur- 
iously in his arm-chair, and sending up thick blue 
wreaths from his pipe. ' For example, observation 
shows me that you have been to the Wigmore Street 
Post-office this morning, but deduction lets me know 
that when there you despatched a telegram.' 

' Right ! ' said I, ' Right on both points ! But I con- 
fess that I don't see how you arrived at it. It was 
a sudden impulse upon my part, and I have mentioned 
it to no one.' 

'It is simplicity itself,' he remarked, chuckling 
at my surprise — ' so absurdly simple that an explan- 
ation is superfluous ; and yet it may serve to define 
the limits of observation and of deduction. Observa- 
tion tells me that you have a little reddish mould 
adhering to your instep. Just outside the Wigmore 
Street Office they have taken up the pavement and 
thrown up some earth, which lies in such a way that 
it is difficult to avoid treading in it in entering. The 



XI OBSERVATION 149 

earth is of this peculiar reddish tint which is found, 
as far as I know, nowhere else in the neighbourhood. 
So much is observation. The rest is deduction.' 

' How, then, did you deduce the telegram 1 ' 

' Why, of course I knew that you had not written 
a letter, since I sat opposite to you all the morning. I 
see also in your open desk there that you have a 
sheet of stamps and a thick bundle of post-cards. 
What could you go into the post-office for, then, but 
to send a wire 1 Eliminate all other factors, and the 
one which remains must be the truth ! ' " 

We are afraid that Mr. Sherlock Holmes fails here 
to justify the tone of somewhat supercilious superiority 
which he adopts towards his friend. He begins by 
pooh-poohing a perfectly accurate remark of Dr. 
Watson, and he ends by a very unsafe inference, for 
he forgets to " eliminate " many factors, such as 
the purchase or the cashing of a postal order. But 
we have quoted the passage because he falls into the 
very confusion between observation and inference — 
or " deduction " as he calls it — which he has under- 
taken to show Dr. Watson how to avoid. In the 
ordinary sense of the words he observed the mud on 
his friend's boot ; he did not observe, but inferred, the 
visit to the post-office. And according to his own 
principles that is where he should have drawn the 
line. 

§ 5. — Our investigation has shown us clearly that observation 
observation is always relative to the previous know- prejudice, 
ledge of the observer, and that it is accurate and 
fruitful exactly in proportion to the thoroughness 
and correctness of that previous knowledge. When 
the previous knowledge is vague and indeterminate, 
the observation is wanting in definiteness and in depth, 
and is unfruitful in inferential results. W^hen instead 
of knowledge, or mixed up with knowledge, there is 



150 



THE LOGICAL BASES OF EDUCATION chap. 



Observation 
and 

Scientific 
Instru- 
ments. 



Experi- 
ment. 



a mass of unfounded belief, the observation is vitiated 
by bias and prejudice. The danger of not keeping out 
this element of error is one against which only the 
trained mind is on its guard. The savage interprets 
all his experiences in accordance with his superstitions, 
and so finds his false beliefs everywhere confirmed by 
his observations. His cattle sicken and die under 
the influence of the " evil eye '' unless he can get a 
stronger counteracting charm thrown over them. In 
these more civilized times men still believe in dreams 
and omens, and support their belief by instances they 
have observed, dwelling on a few cases of more or 
less close resemblance between a dream and some 
following event, and ignoring the enormous number of 
cases in which the dream does not " come true." 
Even the scientific enquirer finds it hard to observe 
quite fairly facts which make against his pet theories. 

§ 6. — The dependence of observation on previous 
knowledge is brought out yet more clearly when 
observation is aided by scientific instruments, which 
all embody whole systems of knowledge. The 
accuracy of observations made with such instruments 
depends on the knowledge which produced the 
instrument as well as on that in the observer's mind. 
And that these are related to each other is shown 
by the fact that only skilled observers can really 
make use of very delicate and complicated instru- 
ments. 

§ 7. — Most strikingly of all is the dependence of 
observation on previous knowledge brought out 
when the observation takes the form of what is 
known as an experiment, that is, is made under cctfi- 
ditions determined by the observer. The selection 
which, in ordinary observation, is merely mental is 
here made physical as well. The object of this 
selection is to omit all elements which have no 



XI OBSERVATION 151 

influence on the phenomenon to be observed, and to 
retain, in known relations to each other, all those 
that have such influence. An error will vitiate the 
whole result, and the history of science is full of 
instances of erroneous conclusions due to the 
presence of unsuspected conditions which modified 
the phenomenon observed. It is evident, then, that 
no one can really experiment who has not extensive 
knowledge of the kind of phenomena he is dealing 
with. Whether he himself arranges the physical 
conditions is immaterial ; the essential thing is that 
he mentally determines those conditions. " Manipu- 
lation of the external world is not of the essence of 
experiment, which simply consists in selection and 
the purpose to observe, usually implying and result- 
ing in precise knowledge of the conditions." ^ 

The advantages of experiment over mere observa- 
tion are its greater definiteness and its subjection to 
control. When we can experiment we can observe 
when we will, without waiting for nature to present 
us with a specimen of the phenomenon we wish to 
study, and thus investigation can go on continuously 
and systematically. Again, when we have the condi- 
tions under our control we can vary them at pleasure, 
and systematically observe the results. In many cases, 
without experiment the knowledge we now possess 
would never have been attained. Many natural 
processes go on so slowly and gently that they escape 
observation. As Lavoisier remarked, the decom- 
position of water had been going on ever since the 
beginning of the world, but had never been observed 
before the experiments of Cavendish and himself 
brought it to light. But experiment is not always 
possible. When the process to be investigated goes 
^ Bosanquet, Knowledge and Reality, p. 35. 



152 THE LOGICAL BASES OF EDUCATION ch. xi 

on very slowly experiment is out of the question. 
The geologist, for instance, cannot experiment on the 
nature of the forces which have made the earth's 
crust what it is, nor the biologist on the evolution of 
species. 



CHAPTER XII 



TESTIMONY 



§ 1. — If we examine the origin of our own know- 
ledge, each one of us will find that by far the 
larger portion of it rests, not on his own personal 
observation, but on the testimony of others. In many 
cases such testimony can be directly tested, and its 
acceptance is then merely a matter of convenience ; 
as, for instance, when a person who has not quitted 
England accepts the testimony of others to the 
existence and characteristics of foreign countries. 
When the testimony is merely the expression of an 
opinion derived by inference from facts easily 
observable, such testing by others is always possible. 
But there are many cases in which facts cannot be 
observed again ; and then the acceptance of testi- 
mony is a matter of necessity, for without it all 
advance in knowledge would be impossible. "The 
uniformities shown in the return of certain of the 
comets are visible only to those who know how to 
rely upon records many hundred years old. The 
uniformities brought to light by statistics are nothing 
to him who cannot depend on an army of co- 
workers." ^ Testimony which can be tested by direct 

^ Ravenshear, Testimony and Authority, Mind, N. S., 
voL vii, p. 66. 



154 THE LOGICAL BASES OF EDUCATION chap. 

observation need not remain testimony, and so need 
not detain us. But we must enquire what tests of 
accuracy it is possible to apply to testimony which 
can never be thus superseded. 

§ 2. — The only testimony of this kind is to 
facts which cannot be again observed. But, as the 
testimony itself records an observation, it might be 
thought unnecessary to say anything further about 
it, and to regard it as simply observation at second- 
hand. This, however, would neglect the factor of 
reception of the testim-ony. When a piece of testi- 
mony is offered, we may either accept it, reject it, 
or remain in doubt about it. In the two former cases 
we make a judgment as to its truth or falsity, and 
every such judgment rests on what seems to us 
sufficient evidence. In the last case we judge that the 
evidence available is not sufficient either to sustain 
or to destroy the testimony. In every case^ then, 
we analyse and criticize testimony offered us, and 
such analysis and criticism is similar in character to 
the inference involved in the analysis and criticism 
of our observations, the difference being that it is 
exercised on judgments made by others instead of on 
facts forming the material of our own judgments. 

As with observation, so with the reception of testi- 
mony, adequate knowledge and freedom from bias 
are essential if the testimony is to mean anything to 
us, and to be fruitful in our hands. Indeed, owing 
to the dependence of the meaning of words and 
sentences on their context, the danger of reading 
into testimony what is only in our own minds is 
even greater than that of falling into the correspond- 
ing error of confusing inference with observation. 
The more remote from our own experiences are the 
events with which the testimony deals, the more 
difficult is it to avoid misinterpretation. This is 



XII TESTIMONY 155 

one reason why so much of the history of remote 
times is of a doubtful character. Another reason is 
the small number of contemporary documents. And 
these react on each other ; for, as the only safeguard 
against misinterpretation is adequate knowledge of 
the times, and as such knowledge itself rests on 
testimony, it is evident that such testimony must be 
supported by testimony, and, consequently, the 
smaller its amount the less is its combined force. 

§ 3. — Having interpreted a piece of testimony as Tests of 
well as possible, the next question is whether it is to mony— 
be accepted or rejected. Here also we must be 
guided by previous knowledge. The savage and the 
child are extremely credulous of all that falls out- 
side the narrow range of personal experience. As 
they have no conception of a systematic universe 
permeated by law, they find in the abnormal and 
the supernatural no contradiction to the accepted 
order of things. And this credulity passes but 
slowly away. Englishmen of the time of James I. 
probably found nothing incredible in Othello's " men 
whose heads do grow beneath their shoulders," and 
the superstitions still common even in the most 
civilized countries include many things equally 
unknown to science. It is, indeed, only the 
specialist in any subject who is a competent judge 
of the value of testimony dealing with that subject. 

Now it is in science that we find the most 
perfect precision and accuracy to which human 
knowledge has yet attained. Science accepts nothing 
on bare authority, and in admitting testimony 
subjects it to the most rigid tests. In addition to 
demanding that freedom from bias, good faith, and 
competence in the observer, with which we dealt in 
the last chapter, science requires that the observation 
shall be recorded immediately it is made, and that 



156 THE LOGICAL BASES OF EDUCATION chap. 

the record shall be both full and precise. This is 
the ideal towards which in other departments of 
knowledge only an approximation is possible. 

In history and in common life the only testimony 
available is generally that of the ordinary 
eye-witness, and is more or less vitiated, not 
only by some or all of the faults of observation, but 
by confusions due to lapses of memory, which are 
supplied, often without the consciousness of the wit- 
ness, by inference or by the play of the imagination ; 
and sometimes even by deliberate fabrication. " The 
evidence which has been adduced for clairvoyance. . . . 
would have hung a hundred men, but before the tri- 
bunal of. science it is as nothing." ^ Even in the law- 
courts where the testimony of the ordinary eye-wit- 
ness is sifted in a way impossible in most other depart- 
ments of life, the standard of acceptance is much lower 
than in science. And this lower standard is 
necessary, for in ordinary life we have to act on 
reasonable presumptions ; were we to demand 
theoretical certainty in every case, life would 
stagnate. " You cannot leave practical matters 
open, to all eternity, as you can matters of specula- 
tive truth." 2 

But though we cannot in most cases wait for 
absolute proof before accepting testimony, yet we 
must have some reasonable guarantee of its accuracy. 
Now, when a statement is false it may evidently be 
so either with or without the knowledge of him who 
makes it ; a man may intentionally say what is untrue 
or may simply be mistaken. The questions as to 
the trustworthiness of the testimony fall then under 
the two general heads of the good faith and the 
accuracy of the witness. The former of these is of 

1 Bosanquet, Knowledge and Reality ^ p. 135. 

2 Ibid., p. 136. 



xii TESTIMONY 157 

logical interest only so far as it bears on the latter, 
that is, so far as our acceptance of the testimony 
rests on considerations as to the truthfulness of the 
witness. If we can test its accuracy independently, 
the question whether the assertor believes it or not 
is of little moment ; so long as a statement is false 
it is not of logical interest to distinguish whether it 
is a falsehood or a simple falsity.^ We are concerned, 
then, with sincerity only in so far as it is evidence 
of accuracy. And this is well, for nothing is so 
difficult to decide as good faith. " * The accent of 
sincerity ' is the appearance of conviction ; an orator, 
an actor, an habitual liar, will put more of it into his 
lies than an undecided man into his statement of 
what he believes to be the truth. Energy of 
affirmation does not always mean strength of con- 
viction, but sometimes only cleverness or effrontery." ^ 
However, in unsupported testimony the question 
of sincerity is important. We must then consider 
whether any of the general conditions which cause 
men to lie are likely to be operative in this case. 
We must ask whether falsehood would appear to 
bring any personal advantage to the witness, whether 
he is likely to be swayed by fear, vanity, sympathy, 
antagonism, the desire to please, or the wish to 
astonish or amuse. We should be inclined to suspect 
all rhetorical flourishes, all dramatic detail, especially 
when any considerable time has elapsed between the 
occurrence of the event and the record of it. 
"Abundance and precision of detail, though they 
produce a vivid impression on inexperienced readers, 
do not guarantee the accuracy of the facts ; they 
give us no information about anything but the 

1 Cf. p. 71. 

'^ Langlois and Seignobos, Introduction to the Study of 
History, p. 162. 



158 THE LOGICAL BASES OF EDUCATION chap. 

imagination of the author when he is sincere, or his 
impudence when he is the reverse." ^ 
Accuracy. Granting the good faith of the witness, we must 
yet accept a narrative as true only when it endures 
certain critical tests. The main points to be considered 
are connected with the competence of the author as an 
observer and as a witness. The essentials of a good 
observer were dealt with in the last chapter. In 
enquiring whether our witness possesses the general 
prerequisite of freedom from bias, we must consider 
what sort of prejudices would be likely to influence 
him, such as those common to his condition in life, 
state of culture, country, and epoch. Especially is 
this important in estimating the value of testimony 
of old writers to the miraculous and extraordinary. 
Often an examination of a writer's works will show 
his dominant superstitions, bias, and prejudices, and 
any statement in which these play a part must be 
discounted accordingly. 

We must next consider the competence of the 
witness as an observer of the particular facts he 
records. And here, in addition to questions as to 
his general competence in observing facts of the kind 
in question, dependent on his special knowledge and 
his power of distinguishing between observation and 
inference, we have to enquire whether he was in a 
favourable condition to observe these particular facts. 
The modern newspaper reporter sometimes writes 
detailed accounts of meetings he has never attended, 
and ancient and modern historians have embelUshed 
their pages with scenes equally dramatic and equall}?- 
imaginative. When the scenes recorded are com- 
plex, much of the detail must be matter of imagina- 
tion, of inference, or of the report of others. For 

^ Langlois and Seignobos, Introduction to the Study of 
History, p. 162. 



XII TESTIMONY 159 

example, when a general records his campaigns and 
his battles it is evident that but a small part of his 
testimony is really based on his own observations. 
Similarly, when a historian relates events which occu- 
pied long periods of time, or describes customs and 
movements which were common over a wide stretch 
of country, he derives much of what he states from 
others. In all such cases, therefore, a large part of 
the testimony which is ostensibly given us by one 
witness is really supplied by an unknown host of 
collaborators, whose good faith and competence we 
have no means of judging. 

But competence as an observer does not always 
imply competence as a witness. Some people seem 
to be constitutionally unable to make an accurate 
statement. " They are subject to ' chronic inac- 
curacy,' a disease of which the English historian 
Froude is a typical and celebrated case. Froude 
was a gifted wi'iter, but destined never to advance 
any statement that was not disfigured by error ; it 
has been said of him that he was constitutionally 
inaccurate. For example, he had visited the city of 
Adelaide, in Australia : ' We saw,' says he, * below 
us, in a basin with a river winding through it, a 
city of 150,000 inhabitants, none of whom has ever 
known, or will ever know, one moment's anxiety as 
to the recurring regularity of his three meals a day.' 
Thus Froude, now for the facts : Adelaide is built 
on an eminence ; no river runs through it ; when 
Froude visited it the population did not exceed 
75,000, and it was suffering from famine at the 
time."^ In fact, however, Froude was right in his 
first two statements. When professedly critical testi- 
mony as to existing facts thus fails us, it is obvious 
that ancient records must be received with caution. 
^ Lauglois and Seignobos, ojp. cit., p. 125. 



160 THE LOGICAL BASES OF EDUCATION chav. 

Probably, however, the most frequent cause of in- 
accurate testimony on the part of competent obser- 
vers is lapse of memory. We all know that memory 
plays lis strange tricks. Details drop out, and too 
often we unconsciously fill the blanks by constructive 
imagination and inference. Or we look at the past 
through spectacles coloured by our personal feelings of 
sympathy and antagonism. We are apt to attribute 
to ourselves the actual utterance of the repartee or 
witticism that has occurred to us later as appro- 
priate to the occasion, and we are constantly liable 
to misconstrue our own motives of action and to 
assume as facts the motives we have attributed to 
others, and from those assumed motives to infer the 
reality of certain conduct. Indeed, if it is difficult 
to distinguish inference of the absent from observa- 
tion of the present, still more hard is it to separate 
inference of the desirable from memory of the actual. 
It is for these reasons that memoirs are so frequently 
distrusted by historians, and that without any reflex- 
ion on the good faith of the writer. To guard against 
these dangers, science demands the immediate record 
of all observations which are to be offered as testi- 
mony to other workers. 

§ 4. — It follows from the above that a good deal 
must be known about a witness before his testimony 
can be received as at all conclusive evidence to any 
fact. When a statement is made anonymously these 
tests cannot be applied. Hence, no rational mind 
attaches any weight to anonymous letters, for all that 
is known of the writer — that he has some reason 
for concealing his identity, and generally wishes to 
injure another person secretly — makes against his 
good faith, and leaves his competence a matter of 
speculation. 

This difficulty of anonymity is very great in his- 



XII TESTIMONY 161 

tory. Unless it can be decided who made a certain 
statement, and when and where it was made, the 
testing of the competence of the witness becomes 
impossible. In modern books these points are 
usually decided by the title-page, or by other internal 
evidence, though even that cannot be held to be decisive 
as to authorship. Eikon Basilike claims throughout 
to be the work of Charles I, though it is quite 
certain that it is nothing of the kind. In the case 
of earlier writings, the question of authorship is often a- 
very difficult one to decide. We all know that, 
in spite of the evidence of the original title-pages, 
valiant attempts have been made to prove that 
Bacon wrote the plays attributed to Shakespeare. 
Without yielding to this wholesale scepticism as to 
our great dramatist, yet it is certain that some 
passages in his works are not by his hand, and 
only criticism can decide which these are. This 
criticism is based partly on the evidence of other 
writers, but mainly on peculiarities of style and of 
structure brought to light by internal examination of 
the text itself. By similar tests the approximate 
dates of the different plays are determined. 

With ancient documents such a criticism is 
even more necessary. Of old writings there are 
usually only copies extant, and these frequently the 
work of ignorant scribes, full of errors, and often 
with forged passages interpolated in the text. Such 
errors and additions can only be eliminated by critical 
comparison of independent documents, that is, of 
documents which are not copies of the same copy. 
The great principle in deciding independence is 
that common errors may be assumed to have a 
common origin. " It is inconceivable that several 
copyists, independently reproducing an original 
free from errors, should all introduce exactly the 

M 



162 THE LOGICAL BASES OF EDUCATION chap. 

same errors ; identity of errors attests community of 
origin." ^ 
Corrobora- § 5. — All Corroboration of testimony, indeed, to 

Testimony. ^6 of value must be independent. The law 
recognizes this, and refuses to accept mere hearsa}^, 
or inference, or evidence which is shown to be the 
result of collusion. Cross-examination is the most 
powerful weapon for detecting falsification, as well 
as for separating observation from inference and 
hearsay. When false testimony is manufactured it 
is apt to be too consistent with itself and more or 
less inconsistent with known facts. As to the first 
point, it is a commonplace of human nature that no 
two persons ever give from memory identical accounts 
of any event they have witnessed in ordinary life ; 
thus, too precise an agreement in details between 
witnesses suggests collusion rather than truth. That 
corroboration is the most above suspicion which 
agrees on the main points, but not on all the details 
of accompanying circumstances. Such concurrence 
of testimony receives additional strength when it is 
evident that the different witnesses have conflicting 
interests, or opposed sympathies, in the matter. 

With regard to the second point, it is very unlikely 
that a manufactured story should take account of 
all the facts it may be brought into relation with, 
and it is in testing it by such facts that a cross - 
examiner shows his skill. Cross-examination is, then, 
a valuable process of sifting the true from the false 
in oral testimony, though it has its own peculiar 
danger. A question nearly always suggests a certain 
kind of answer, either by its form, or by the context 
in which it occurs, or by the manner and tone of the 
questioner. This suggestion acts unconsciously on 
the mind of the person questioned and tends to 
^ Langlois and Seignobos, op. cit., p. 8L 



XII TESTIMONY 163 

modify the answer given. Some questions, of course, 
do this more markedly than others, and in the law 
courts these are ruled out by the judges as "leading 
questions." 

Cross-examination cannot, however, be applied to 
the dead authors of historical documents. We 
must, therefore, test their accuracy by certain more 
or less general considerations. Any of their state- 
ments may be accepted as probably true when the 
facts are such as to reduce liability to error or 
deception to a minimum. If the author had no con- 
ceivable motive to lie, or if the fact asserted was in 
itself so prominent as to make detection of falsehood 
certain, or was in opposition to the writer's known 
prejudices and wishes, then we may accept the record 
as being as near certain truth as the nature of the 
case will allow. 

Most historical testimony, however, itself rests on Tradition, 
testimony. Our aim is to get back to the record of 
the original observer ; but this is very often impos- 
sible. Now, if the testimony is simply passed on 
through a chain of witnesses, fresh chances of error 
are introduced at each link, and each successive 
witness is of less worth than his predecessor ; the 
longer the chain the weaker the evidence of the last 
link. This is the case with documents copied one 
from the other; each reproduces the errors of its 
predecessors, and probably introduces some new ones 
of its own. But this liability of error is enormously 
increased when the testimony is oral. It is a well- 
known parlour game, but one which well illustrates 
our point, to relate secretly a written story to the 
first of a ring of people, who similarly passes it on 
to the second, and so on, till the last tells the story 
aloud, or better still, writes it and reads it aloud. 
The comparison of this last version with the first 

M 2 



164 THE LOGICAL BASES OF EDUCATION chap. 



will be instructive to those who are disposed to accept 
all testimony given in good faith as certainly true. 

When oral tradition passes on from generation to 
generation the variations become more marked ; yet it 
is in this legendary form that the earliest history of 
all peoples comes down to us. Quite evident is it 
that we are unjustified in accepting any such legends 
as true ; they may contain some truth, but it is cer- 
tain they contain much error, and there are no means 
of sifting the true from the false. As Niebuhr says, 
a legend is " a mirage produced by an invisible object 
according to an unknown law of refraction." ^ 
Legends embody a people's ideas, but cannot be 
appealed to as records of facts. 

In other cases, however, the testimony of various 
witnesses support each other, either directly by 
recording the same fact independently, or by one set 
of witnesses testifying to the credibility of others. 
" In the acceptance of Livingstone's accounts of the 
countries through which he passed, are not the 
relevant grounds in part the esteem in which he was 
held by his contemporaries, coupled with their cre- 
dentials ; in part the credentials of the societies 
and other media of record and publication through 
which his work has in successive stages come to the 
individual reader ? If I submit myself to the knife 
of the surgeon, how have I assured myself that 
he will do the right thing, unless by relying upon a 
complex tissue of testimony as to the professional 
ability of a large number of persons 1" ^ 

§ 6. — One last point must be noticed, and that is 
the danger of inferring from mere absence of testi- 
mony to non-existence in fact. Even in the present, 
absence of observation does not prove absence of 



Quoted by Langlois and Seignobos,' op. cit. 
■2 Kavenshear, op. cit., pp. 82—83. 



182. 



XII 



TESTIMONY 165 



existence. Every scientific discovery is, indeed, testi- 
mony to the contrary. Within the last few years, 
for instance, several gases whose existence had pre- 
viously been unsuspected even by scientific experts, 
have been discovered in the atmosphere. A state- 
ment should be accepted on negative evidence only 
when the most careful precautions have been taken 
to secure the greatest possible completeness of that 
evidence. Darwin established on negative evidence 
that certain orchids secrete no nectar, but he only 
accepted the conclusion when he had observed the 
plants in question under every variety of circumstance 
that could affect the result.^ 

Still more dangerous is it to infer that an event 
never occurred in the past because no record of it 
now remains. To render this probable we must 
have grounds for knowing that no such record ever 
did exist, and that the event would certainly have 
been recorded had it occurred. This much narrows 
the scope of the inference. When an author sets 
out to give a systematic account of a class of facts, 
we may assume that any fact of that kind which he 
does not mention did not exist, if that fact was such 
that it could not have escaped his notice had it 
existed, and must have been seen by him to be per- 
tinent to his record. In all other cases we can only 
suspend judgment and confess our ignorance. 

^ Cf., Darwin, Fertilization of Orchids, pp. 38—39. 



CHAPTER XIII 



HYPOTHESES 



Nature of § 1. — All reception of facts, whether by observa- 

ypo tses. ^.^^ ^^^ from testimony, challenges the mind to fit 
them into a system by relating them to each other 
and to the totality of knowledge already possessed. 
The answer to this challenge is a hypothesis, or 
supposed relation suggested by the facts themselves. 
The likelihood of such a supposal being true is, of 
course, largely dependent on the knowledge of the 
mind that makes it. The savage assumes magic and 
supernatural agency where the scientist looks for 
natural causation. All attempts at the organization 
of facts into knowledge proceed, however, by way 
of hypothesis. Even simple recognition of an 
object is of the nature of hypothesis, though in 
most cases verification is immediate.^ In ordinary 
life we are always making hypotheses. I go to 
catch a train, and I act on the hypothesis that the 
railway service is uninterrupted ; I sit down to 
write this chapter guided by the supposition that my 
mind will follow a certain consecutive train of 
thought. These are hypotheses, for they are not 
1 Cf. pp. U6— 147. * 



CH. XIII HYPOTHESES 167 

certainties. A fog or an accident may dislocate the 
railway service, and the state of one's health or some 
powerful disturbing circumstance may render con- 
secutive thought impossible. 

Every supposition, then, as to the relations of 
facts is a hypothesis, whether it is made in ordinary 
life or in science. But as scientific thought differs 
from other thought only in its greater precision, the 
nature and uses of hypotheses will be best studied 
in connexion with scientific examples. It may be 
said, indeed, that the special work of science is the 
testing and verification of hypotheses, for, as 
Herschel says, " We must never forget it is prin- 
ciples, not phenomena — the interpretation, not the 
mere knowledge of facts, — which are the objects of 
enquiry to the natural philosopher." ^ 

§ 2. — Hypotheses are suggested by facts, but 
they may be suggested in an indefinite number of 
ways. No rules can be given for forming them, and 
not every enquirer is equally prolific in hypotheses 
which turn out to be real " guesses at truth." 
Indeed, the great masters of science are marked 
above all else by an insight into the reasons of 
things at which the ordinary searcher after know- 
ledge can only wonder. In this sense, a great 
scientist, like a poet, is "born, not made." "The 
inventor of hypotheses, if pressed to explain his 
method, must answer as did Zerah Colburn when 
asked for his mode of instantaneous calculation. 
When the poor boy had been bothered for some 
time in this m^anner, he cried out in a huff, ' God 
put it into my head, and I can't put it into yours.' " ^ 

But knowledge also plays a part. A fact which 
means nothing to the unprepared mind may suggest 

^ Discourse on Natural Philosophy, § 10. 
'•^ De Morgan, Budget of Paradoxes, p. 56. 



168 THE LOGICAL BASES OF EDUCATION chap. 

a far-reaching hypothesis to the mind which is stored 
with appropriate knowledge and governed by an 
appropriate interest. Thus the common experiences 
of falhng bodies and of the motions of the moon 
suggested to Newton the great theory of gravitation. 
Some discoveries, it is said, are made by accident ; 
but such accidents only happen to those who are 
prepared to interpret them. Many crystals had 
been broken in the world before the accidental 
fracture of one suggested to the physicist Haiiy the 
laws of crystallization. 

As science advances, more and more discoveries are 
due to attempts to explain small deviations between 
observed facts and established laws. For example, 
the planet Uranus was observed to deviate from its 
calculated path, and to account for such deviations 
the hypothesis was formed that a hitherto unknown 
planet revolved round the sun at a still greater 
distance from it than Uranus. From the observed 
positions of Uranus the position of this sujDposed 
planet was calculated. Search with the telescope 
in that direction proved the accuracy of the .hy- 
pothesis, and the new planet was named Neptune. 
In quite recent years an investigation suggested by 
a small unexplained difference between the weight 
of nitrogen obtained in the chemical laboratory and 
the gas which had hitherto been supposed to be 
pure nitrogen in the atmosphere, led to the dis- 
covery of argon. Many other instances could be 
given, but these are sufficient to show that in such 
cases not even the problem could suggest itself to a 
mind not conversant with the advances already made 
in the appropriate branch of knowledge. 

§ 3. — Hypotheses, then, are suggested by facts to 
the mind prepared to interpret them. It does not 
follow, however, that the greater the number of 



xni HYPOTHESES 169 

facts, the more likely the hypothesis is to be right. 
The great difficulty always is to pick out the 
essential from the merely accidental in the whole 
mass of circumstances. Reality does not give us 
phenomena already sorted and selected, as the 
teacher of science presents them to his pupils in the 
class-room, and the main difference between the 
successful discoverer and the unsuccessful worker 
lies just in the power to see what may safely be 
neglected. But too great a wealth of facts increases 
this difficulty, for each new fact brings in some fresh 
attendant circumstances. This is very well put by 
Dr. Conan Doyle in the Memoirs of Sherlock Holmes. 
After Mr. Holmes had solved the problem of the 
Naval Treaty he says : " The principal difficulty . . . 
lay in the fact of there being too much evidence. 
What was vital was overlaid and hidden by what 
was irrelevant. Of all the facts which were pre- 
sented to us, we had to pick out just those which 
we deemed to be essential, and then piece them 
together in their order, so as to reconstruct this 
very remarkable chain of events." 

When, indeed, we can get what is called a " pure 
case," that is, an instance in which only those con- 
ditions are present which we are investigating, then we 
can immediately assert the relation from one instance, 
and that, not as a more or less probable hypothesis, 
but as a certain truth. In mathematics we can do 
this, for we entirely determine the operative con- 
ditions ; our triangles, circles, &c., are ideal and 
perfect, and we infer their consequences from single 
cases. If, for example, we prove that one right- 
angled triangle is inscribable in a semi-circle, this 
proof depends only on the ideal nature of our 
figures, and is consequently applicable to every 
possible example in so far as it fulfils these 



Bias, 



170 THE LOGICAL BASES OF EDUCATION chap. 

conditions. Thus our generalization is the immediate 
result of our construction.^ But with concrete objects 
we cannot do this so thoroughly. In chemistry, it is 
to some extent possible. So long, for example, as the 
chemist means by ' water ' nothing but absolutely pure 
water, what he finds true of one drop he can affirm 
to be true of every other drop. But the actual 
water in nature contains all kinds of impurities in 
very various amounts, and it is very difficult to get 
a pure case even here. It is, then, because nature 
only presents us with relations in "a tangle of 
many threads which science has to unravel " ^ that 
we must resort to hypotheses. 
Danger of This resort, however, has its own danajers. Having 
guessed at an explanation, the mind naturally wishes 
to find it true, and thus there is the danger of bias 
in observing facts which bear on the hypothesis — 
the attitude of. mind expressed by the saying, "if 
the facts do not agree with the theory, so much the 
worse for the facts." As Jevons truly says, " it is 
difficult to find persons who can with perfect fair- 
ness register facts for and against their own peculiar 
views." ^ 

Nor is this the only danger. To infer the conse- 
quences of a hypothesis is generally a task of no 
great difficulty, whilst the careful testing and verifica- 
tion of a hypothesis by analysis of facts is laborious 
and often both difficult and tedious. There is, then, 
a temptation to be satisfied with the former process, 
and when this is yielded to, the result is the con- 
struction of elaborate systems of the universe out of 
all relation to fact. It is this tendency to substi- 
tute guess-work for real investigation, and imagination 

1 Cf. p. 132. 

2 Hobhouse, The Theory of Knoidedge, p. 328. 
2 The Principles of Science, p. 402. 



XIII HYPOTHESES 171 

for observation, which has made the ordinary ' prac- 
tical man ' so suspicious of what he calls ' theory,' 
and so fond of contrasting it with ' practice,' and of 
telling us that " an ounce of fact is worth a ton of 
theory." No doubt this is so if the ' fact ' is true 
and the ' theory ' false, but between true theory 
and real fact there is no opposition at all. 

§ 4. — The formation of a hypothesis, then, must Testing of 
not be taken as the establishment of a truth. All ^^"^ ^'^^^" 
hypotheses must be held subject to revision, to 
modification, even to rejection, should further know- 
ledge of fact demand it. For though it is true 
that one single case is seldom sufficient to establish 
a hypothesis, it is equally true that one single fact 
which can be shown to be really in contradiction 
to a hypothesis overthrows it. Indeed, it is com- 
paratively seldom that the first hypothesis suggested 
to the mind is the true one. Kepler records that 
he tried and rejected nineteen hypotheses before 
he hit on the laws of the motions of the planets 
round the sun. Similarly, in the discovery of argon 
two hypotheses were tried and rejected before the 
third one — that a hitherto unknown element exists 
in the atmosphere — was found to be verified by the 
facts. 

False hypotheses, as well as true ones, are suggested 
by analogies between the new facts and facts whose 
relations are already known. It is the extreme 
complexity of nature which makes a plurality 
of hypotheses possible. Sometimes several possible 
hypotheses occur to the mind at once, at other times 
they occur successively, and, it may be, at long intervals 
of time. But whenever they occur, scientific hypo- 
theses are always grounded on some characteristic of 
the facts : they are never mere random guesses. 

§ 5. — Because a hypothesis is finally rejected it 



172 THE LOGICAL BASES OF EDUCATIOI^ chap. 



does not, however, follow that it has been worthless 
in the advance of science. It may, in its time, have 
furnished a fairly accurate description of the per- 
ceived facts with which it dealt. "Although the 
Ptolemaic doctrine is now known to be framed on an 
utterly extravagant estimate of the true place of the 
earth in the scheme of the heavens, yet the apparent 
movements of the celestial bodies are accounted for 
by the theory with considerable accuracy." ■*■ 

Often a hypothesis is of a merely descriptive 
character, and is a more or less figurative way of 
expressing some abstract relation whose concrete 
terms are really unknown. It was, in this way, long 
customary to speak of the " electric fluid," though 
the existence of a material " fluid " w^as not implied, 
because the rapid and easy motion of a fluid was the 
nearest analogy to the known action of electricity. 
In a similar way many scientists for a long time 
regarded the atomic theory, which plays so large a 
part in modern chemistry, " as a kind of symbolism 
by which different chemical elements could be char- 
acterized, their compounds described, and the actual 
weights practically calculated. . . . Although . . . . 
chemical research was governed all through the 
century by the atomic view of matter, it does not 
appear that philosophers considered the existence and 
usefulness of chemical formulae as a proof of the 
physical existence of atoms, or of smallest indivisible 
particles of matter, in the older sense of the theory." ^ 

Often hypotheses are put forward as mere woi'hing 
hypotheses^ that is, guides to further enquiry. When 
a complex mass of phenomena is before us for analysis 
we must begin somewhere in our task of disentang- 

^ Ball, Story q/ the Heavens, p. 6. 

2 Merz, History of European Thought in the Nineteenth 
Century, vol. i., pp. 17 — 20. 



XIII HYPOTHESES 173 

ling its threads. Any hypothesis is better than none, 
so long as it fairly expresses the facts already 
examined. Hence, in every branch of science pro- 
visional hypotheses have guided investigation, though 
it was known that they did not exactly express the 
truth. " The theory of the two fluids in electricity 
did good service for a long time in enabling philoso- 
phers to define their ideas, to describe, calculate, and 
predict phenomena. In optics, the so-called corpus- 
cular theory of light is still used with advantage as 
a convenient means of summarizing the laws of 
reflection and refraction." ^ 

§ 6. — Any hypothesis, then, is permissible which 
is sufficiently definite to allow its consequences to be 
deduced, and which is not inconsistent with itself or 
with any fully established law of nature. Even this 
last condition must be jealously scrutinized, for it has 
often happened that a new hypothesis has been true, 
though it was in conflict with what had previously 
been regarded as established knowledge. The 
Copernican theory that the daily motion of the 
heavenly bodies round the earth was only apparent, 
and in reality due to the daily rotation of the earth 
on its own axis, was in direct conflict with the 
Ptolemaic doctrine that the earth was absolutely fixed 
and immovable. But, as had, indeed, been seen 
by Ptolemy himself, the perceived facts could be 
explained on either hypothesis. The new theory, 
therefore, was not, so far, in real conflict with what 
was actually known, but only with an alternative 
way of explaining the known phenomena. Copernicus 
supported his view by showing that the Ptolemaic 
hypothesis " would attribute an almost infinite 
velocity to the stars, and that the rotation of the 
entire universe around the earth was really a prepos- 
' Merz, op. cit., p. 422. 



174 THE LOGICAL BASES OF EDUCATION chap. 

terous supposition." ^ But when Copernicus took the 
second great step of denying to the earth that 
central position in the universe which for centuries 
had been assigned to it, a complete revolution in 
men's systems of knowledge was demanded. Nor 
was this revolution confined to astronomy, for the 
belief that the earth was the centre of all things had 
naturally exercised a considerable influence upon 
man's conception of his own importance, and these 
flattering ideas must now be considerably modified. 
Soon after the announcement of the Copernican 
hypothesis the invention of the telescope enabled 
men to increase enormously the number of facts 
which a true theory of the heavenly bodies must 
explain. It was the opposition between these facts 
and the Ptolemaic hypothesis, and their agreement 
with the Copernican hypothesis, which finally decided 
between these rival explanations. 
Crucial § 7. — So, in every case, it is fact alone which can 

decide between rival hypotheses. A fact which is thus 
decisive in that, at one and the same time, it disproves 
one hypothesis and confirms another, is called a 
Crucial Instance, and an experiment which exhibits 
such an instance is a Crucial Experiment. " Thus 
the phases of Yenus, similar to those of the moon, 
but concurring with great changes of apparent size, 
when discovered by Galileo, presented a crucial 
instance in favour of the Copernican hypothesis, as 
against the Ptolemaic, so far at least as to prove 
that Yenus revolved around the sun inside the orbit 
of the earth." ^ 

The history of science contains many beautiful 
examples of crucial instances and experiments. Some 
of the most interesting were experiments designed 

1 Ball, The Story of the Heavens, p. 7. 

2 Carveth Read, Logic, Deductive and Inductive, p. 217. 



XIII HYPOTHESES 175 

to decide between the two great rival theories as to 
the nature of light. According to Newton's corpus- 
cular theory, luminous bodies actually emit exceed- 
ingly minute particles in all directions and at an 
enormous rate of speed. " A very different hypothesis 
had, however, been suggested about the same period 
by Huyghens, who supposed light to be produced in 
the same manner with sound, by the communication 
of a vibratory motion from the luminous body to a 
highly elastic fluid, which he imagined as filling all 
space, and as being less condensed within the limits 
of space occupied by matter, and that to a greater or 
less extent, according to the nature of the occupying 
substance. Thus, in place of anything actually thrown 
off, he substituted waves or vibrations, propagated in 
all directious from luminous bodies, through this 
medium, or ether, as he called it."^ For a long time 
these rival hypotheses divided the scientific world, 
for each explained in a remarkable manner the 
known laws of reflection and refraction. To decide 
between them it was necessary to infer from the two 
hypotheses consequences contradictory to each other, 
and then to appeal to observation to show which of 
these agreed with fact, Now, " if the undulatory 
theory be true, light must move more slowly in a 
dense refracting medium than in a rarer one ; but 
the Newtonian theory assumed that the attraction 
of the dense medium caused the particles of light to 
move more rapidly than in the rare medium. On 
this point, then, there was complete discrepancy 
between the theories, and observation was required 
to show which theory was to be preferred. Now, by 
simply cutting a uniform plate of glass into two 
pieces, and slightly inclining one piece so as to 
increase the length of the path of a ray passing 
^ Herschel, Discourse on Natural Philosophy, § 276. 



176 THE LOGICAL BASES OF EDUCATION ch. xiii 

through ifc, experimenters were able to show that 
light does move more slowly in glass than in air." ^ 
Other crucial experiments also supported the undu- 
latory theory and negatived the corpuscular, so that 
the former may now be regarded as completely 
established. 

^ Jevons, The Pi^incijyles of Science, p. 52L 



CHAPTER XIV 



DIRECT DEVELOPMENT OF HYPOTHESES 



§ 1. — All hypotheses, as we saw in the last 
chapter, are suggested by facts, but only to the 
mind prepared to interpret them. We must now 
examine the logical character of the inference in- 
volved in the formation and gradual development of 
hypotheses. 

Every hypothesis is a suggested universal relation, 
for a scientific conception of the universe excludes 
all idea of mere casual occurrence. But though 
every fact can be ultimately accounted for by its 
relations, yet two or more facts may occur together, 
and so be related in time or space, without having 
"any necessary connexion with each other. As 

" A raven cried ' Croak,' 
And they all tumbled down." 

A suggestion that the falling was due to the croak- 
ing would be on quite as high a scientific level as 
are the beliefs in charms and magic which play so 
large a part in the lives of the superstitious. Such 
agreements in time of occurrence are merely acci- 
dental coincidences. By styling them ' accidental ' 

N 



Accidental 
Coin- 
cidences 
and 

Necessary 
Connexions 



178 



THE LOGICAL BASES OF EDUCATION chap. 



Empirical 
Generaliza- 
tion and 
Enumera- 
tive In- 
duction. 



no more is meant than that they have no necessary 
connexion with each other. One of the greatest 
difficulties of the search after knowledge is to 
distinguish between such coincidences and real 
connexion. It is the latter that is always suggested 
by a hypothesis, for only on the basis of necessary 
connexion can a universal relation be asserted. But 
even when an observed relation is really the ex- 
pression of such a connexion, yet that relation may 
not always occur, for its expression in fact may be 
frustrated by the presence of other relations, them- 
selves equally universal. Particular occurrences are 
all due to the combination and inter-action of 
universal relations which may support or hinder 
each other. Hence, the non-recurrence of a relation 
once observed is itself a fact to be accounted for by 
reference to other universal relations. In other 
words, the ground of a negation is equally universal 
with that of a positive relation. 

§ 2. — From the beginning of life the mind has a 
tendency to generalize its observations on very in- 
sufficient evidence. This merely means that there 
is at first no conception of the infinite complexity of 
reality and of the enormous number of conditions 
which may interfere to modify or hinder the ex- 
pression in fact of a given relation. This tendenc}^ 
to generalize is both helped and guided by the use 
of language. Certain instances are observed to 
agree in possessing a particular attribute, or in acting 
in a certain way ; and the direction in which this 
observed relation is generalized, and the extent to 
which that generalization is carried, are determined 
by the general idea, or concept, under which the 
observed instances are thought. For example, copper 
and iron are observed to expand when heated ; and 
the mind tends immediately to generalize that 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 179 

relation. But whether the generalization suggested 
is, that ' metals ' expand when subjected to heat, or 
that ' solids ' so expand, depends upon which of those 
general ideas occurs to the mind. So, in every case, 
what hypothesis is actually suggested is determined 
by the conception under which the instances are 
thought. Here comes in the first great difficulty in 
an inductive enquiry. All particular instances can 
be thought under an indefinitely large number of 
general ideas, some of which are represented in 
language by separate names, whilst others are not. 
Those so represented naturally occur first to the un- 
trained mind, and those represented by nouns substan- 
tive first of all. But the idea covered by such words 
is always of a very concrete and complex character, 
whilst every relation is abstract, in that it is 
determined, not by the whole concrete nature implied 
by the name, but by some special element in that 
nature. A hypothesis, therefore, guided by a common 
noun will never explain the relation, and indeed 
will never even state it exactly ; it only gives the 
first and most obvious result of a superficial ob- 
servation. This step may be represented symbolically 
thus — 

Instances a, b, c, d, agree in possessing P, 
But a, b, c, d, are instances of the class S ; 
Therefore, S may be P. 

Here it will be seen we have a syllogism in the 
third figure, with S undistributed in the premises. 
We are, therefore, not justified in drawing as our 
conclusion the definite statement that S is P, but 
only as suggesting such a universal relation as a 
hypothesis worthy of consideration. 

Two kinds of evidence in support of this suggested 
universal are conceivable. The one which first 

N 2 



180 THE LOGICAL BASES OF EDUCATION chap. 

occurs to the untrained mind is to attempt to 
examine every case of S. This is what is meant by 
Induction hy Simple Enumeration^ of which Bacon 
truly said it "is a puerile thing, and concludes 
uncertainly, and is exposed to danger from any con- 
tradictory instance." ^ In all cases of the slightest 
importance it is evident that the examination of 
every instance is an impossibility. But even were 
it attainable the result would not be the establish- 
ment of a true universal relation. For it is only 
when a necessary connexion of content is shown 
that a relation can be affirmed as absolutely univer- 
sal, and a mere summation of instances deals with 
nothing but their numerical aspect, and no ground 
of necessity can ever be found in simple counting. 
Analogy. § 3. — We must, then, regard this step as only a 
first preliminary to the selection of a more exact a.nd 
abstract general idea under v/hich to think our 
instances. To find this we proceed to analyse them 
till we detect some element which seems to us a 
possible ground of the observed relation. This takes 
us to the form of argument known as Analogy^ where 
the selected element naturally becomes the predicate 
in each of our premises and the inference falls into 
the second syllogistic figure — 

P possesses the character M, 

These instances of S also possess the character M ; 
Therefore, these instances of S may be instances 
of P. 

Again we see that no certain conclusion can be 
drawn, because our middle term is not distributed in 
either premise. Our conclusion is still, then, only a 
hypothesis, but it is a hypothesis ha^dng a greater 
probability than at the end of the first step, because 
^ Novum Organum, bk. i., § 105. 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 181 

we have in M a suggested ground of the observed 
relation. The hypothesis would now be most com- 
pletely expressed by " M may be the ground of the 
relation of S and P," or by the equivalent hypothetical 
form " If S is M it may be P." 

It is evident that the whole value of such a 
hypothesis depends upon whether M is really 
important to the suggested relation between S and P. 
Directly we can prove that M is actually the 
ground of this relation, our argument ceases to be 
analogical and becomes demonstrative, our conclusion 
passes from a supposition or hypothesis into an 
established truth. The process of such proof must 
be examined later; we are now concerned to 
emphasize the point that the value of an analogical 
argument, that is, the degree of probability attaching 
to its conclusion, depends entirely on the im- 
portance of the selected middle term M. 

All analogy is argument from resemblance ; from 
observing a certain quality in things of a particular 
kind we infer that the same quality will be possessed 
by other things of that kind. Such inferences are 
of very various degrees of worth, proportioned to 
the importance of the resemblance on which they 
are based. And what is important from one point 
of view is unimportant from another ; resemblances 
from which we might plausibly infer athletic prowess 
might only mislead if our inference were to intellec- 
tual ability. Nor are the resemblances which first 
attract notice necessarily the most important for our 
purpose. The resemblances between sponges and 
marine plants are obvious, and yet an inference to 
the nature of sponges based on that resemblance 
would be entirely wrong. We frequently hear the 
argument that a nation is like a man, subject to 
periods of growth, maturity, and decay, in necessary 



182 THE LOGICAL BASES OF EDUCATION chap. 

sequence on each other, and the conclusion is 
regarded as certain. Now, no conclusion from mere 
analogy, as we have seen, can be certain, but in this 
particular case it is doubtful if it is even of any 
great strength. As Burke well put it : "I am not 
quite of the mind of those speculators who seem 
assured that necessarily, and by the constitution of 
things, all states have the same periods of infancy, 
manhood, and decrepitude, that are found in the 
individuals who compose them. Parallels of this 
sort rather furnish similitudes to illustrate or to 
adorn, than supply analogies from whence to 
reason. The objects which are attempted to be 
forced into an analogy are not found in the same 
classes of existence. Individuals are physical beings 
subject to laws universal and invariable. The 
immediate cause acting in these laws may be 
obscure : the general results are subjects of certain 
calculation. But commonwealths are not physical 
but moral essences. They are artificial combinations, 
and, in their proximate efficient cause, the arbitrary 
productions of the human mind. We are not yet 
acquainted with the laws which necessarily influence 
the stability of that kind of work made by that 
kind of agent." ^ 

Nor should very considerable differences in out- 
ward appearance lead to the assumption that there 
is no hidden, but essential, identity. Dr. Wallace 
gives a most striking instance, in which not only the 
common observer but even the very elect of botanical 
specialists had for long been misled by such 
differences. "All the cucumbers and gourds vary 
immensely, but the melon {Cucumis melo) exceeds 
them all. A French botanist, M. Naudin, devoted 
six years to their study. He found that previous 
^ Letters on a Regicide Peace, Works, vol. viii., pp. 78 — 79. 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 183 

botanists had described thirty distinct species, as 
they thought, which were really only varieties of 
melons. They differ chiefly in their fruits, but also 
very much in foliage and mode of growth. Some 
melons are only as large as small plums, others weigh 
as much as sixty-six pounds. One variety has a 
scarlet fruit. Another is not more than an inch 
in diameter, but sometimes more than a yard in 
length, twisting about in all directions like a serpent. 
Some melons are exactly like cucumbers ; and an 
Algerian variety, when ripe, cracks and falls to 
pieces, just as occurs in a wild gourd." ^ 

Such an example brings out clearly that the 
strength of an analogy cannot be calculated from the 
amounts of outward resemblance and difference 
between the cases, because the resemblance really 
important for the purpose in view may be a hidden 
one. This shows why it is that full and appropriate 
knowledge bears such an important part in the 
framing of hypotheses worthy of investigation. Were 
the strength of the analogy dependent only on the 
amount of outward likeness, the framing of fruitful 
hypotheses would require mainly a pair of good eyes, 
and the work of induction would be something very 
different from the task of enormous difficulty and 
complexity it really is. It is because the grounds of 
the relations we observe are not only hidden, but 
often even disguised, that the advance of knowledge 
is slow, even though the greatest of human intellects 
are engaged in helping it forwards. 

Of course, when knowledge is not sufficiently 
advanced to determine the relative importance of 
points of resemblance and difference, it is necessary 
to work with the material at hand. For example, 
in the early stages of electrical science, " Franklin 
^ Darwinium, pp. 87 — 88. 



184 



THE LOGICAL BASES OF EDUCATION chap. 



enumerates specifically an agreement between 
electricity and lightning in the following respects : — 
Giving light ; colour of the light ; crooked direction ; 
swift motion ; being conducted by metals ; noise in 
exploding ; conductivity in water and ice ; rending 
imperfect conductors ; destroying animals ; melting 
metals ; firing inflammable substances ; sulphureous 
smell (due to ozone, as we now know) ; and he had 
previously found that needles could be magnetized 
both by lightning and by the electric spark. He 
also drew attention to the similarity between the 
pale blue flame seen during thundery weather playing 
at the tips of the masts of ships (called by sailors St, 
Elmo's Fire), and the 'glow' discharge at points."-^ 
Here some of the resemblances are magnetic, and 
therefore, important, but others, such as the colour 
and smell, did not, by themselves, lend much support 
to the hypothesis of identity of nature between 
lightning and electricity. With the advance of any 
science the hypotheses suggested in it tend to become 
continually more probable, because the increase of 
knowledge enables a clearer distinction to be drawn 
between the weakness and strength of the analogies 
on which they are based. 

§ 4. — A hypothesis having been suggested by 
analogy it must be brought to the test of fact for 
confirmation or denial. But no hypothesis must be 
regarded as a fixed and unchangeable formula. 
Though it may be on the whole supported by further 
observations, yet it frequently undergoes many 
modifications before it attains the form in which it is 
finally accepted. The aim is to analyse the concrete 
and complex facts of experience so as to disentangle- 
the universal and abstract relations which are com- 

^ S. Thompson, Elementary Lessons on Electricity and 
Magnetism, 2ncl Edition, p. 254. 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 185 

bined in them. Every such relation is always over- 
laid with all kinds of attendant circumstances, some 
of which are indifferent to it whilst others are not. 
The task of induction is to separate from all this 
irrelevant mass of material the relation expressed by 
the hypothesis which guides the enquiry, so as to find 
what it is in itself, independently of all interfering 
conditions. 

When the hypothesis deals with a simple causal 
sequence, the whole of which is open to observation, 
this task can be to some extent carried out directly 
by certain inductive methods which were first clearly 
formulated by Mill, as the results of his analysis of 
the methods of enquiry in physical science set 
forth by Herschel in his Discourse on Natural 
Philosophy. These methods can deal only with 
phenomena directly perceptible by the senses, and, 
hence, cannot reach those more hidden laws which 
express the most fundamental relations. As Dr. 
Venn says : "It is very important that the student 
should clearly recognize that these Inductive 
Methods, which play so important a part in our 
logical treatises, are not of a rigidly scientific 
character. They belong rather to what may be called 
the plane or level of popular enquiry. . . , These 
Methods are nothing more than practical applications 
of the Law of Causation when this is interpreted in a 
popular scientific form." ^ But this does not destroy 
their practical utility. In all the ordinary affairs of 
life we are content with even less confirmation than 
these methods can suppl}", and in science itself they 
play an important part in the suggesting, testing, 
and moulding of hypotheses. 

As applications of a view of causation, half scien- 
tific and half popular, the methods assume that every 
^ Empirical Logic, p. 420. 



186 THE LOGICAL BASES OF EDUCATION chap. 

event has a cause, that the same cause always tends to 
produce the same effect, and that an effect is related 
in energy to its cause. But as the only causes they 
deal with are those open to sense-perception they 
cannot assume that the same effect is always due to 
the same cause, for as we have seen, this identity of 
the causal relation is often found only when we get 
behind sense-perception to the hidden reality which 
the perceived facts more or less adequately express.^ 

With these limitations the methods all aim at 
eliminating from the concrete facts all elements 
which are indifferent to the relation under investi- 
gation. Their fundamental principle is that what- 
ever cannot be removed without altering the observed 
phenomenon is a condition of its occurrence, and 
whatever can be so withdrawn is in no essential 
connexion with it. As corollaries from this, and 
special expressions of the postulate that cause and 
effect are related in energy, are the more special 
principles that elements which sliow corresponding 
variations in amount or intensity are causally con- 
nected, whilst if the increase or decrease of the one 
is not attended by a similar variation in the other 
they do not form a causal sequence ; and that any 
difference in amount between phenomena regarded as 
cause and effect presents a further problem for 
investigation. 

These principles may be expressed symbolically 
by the formulae A B — xy ; AC — xz, v/here any 
of the letters may represent a whole complex 
of elements. Then, as B can be removed without 
affecting x, it is assumed that B — x is not a causal 
sequence, whilst as the removal of B is attended by the 
disappearance of y, it is inferred that B and y are 
causally connected. The inference involved may be 
1 Of., p. 36. 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 187 

expressed in two syllogisms ultimately resting upon 
the second axiom of causation, thus — 

Any cause is always followed by the same effect, 
A is followed in this case by x and y ; {1st formula) 
Therefore A is always followed by either x or y. 
Then, taking this conclusion as a premise — 
A is always followed by either x or y. 
But A is not always followed by y ; (2nd formula) 
Therefore A is always followed by x. 
This brings out the fact that the whole argument 
becomes precise and definite only by the use of the 
negative instance which excludes A — y as a causal 
sequence. The validity of the whole inference 
evidently depends upon the truth and sufiiciency of 
the actual premises which are here represented sym- 
bolically. The use of such symbols, however, disguises 
the greatest difficulty of the whole process, for we 
cannot get to any premises which may be fairly 
represented by them till we have done much of the 
work of induction. Nature does not present us with 
definite sets of distinct elements standing in known 
relations to each other. We, therefore, do not start 
with anything corresponding to the symbolic formulae ; 
but rather, the filling up of those formulae is the 
result of analysing a process already more or 
less completed. But though this is true, yet the 
purpose of so arranging the facts as to fulfil the 
conditions of the formulae is operative throughout, 
and the actual process consists in a gradual approxi- 
mation to such definite arrangement. 

Lastly, it must be remembered that though for the 
sake of clearness in exposition, the inductive methods 
will be treated separately, yet in any full inductive 
enquiry they are used together in any combination, 
and, as the symbolic statement shows, they are all 
expressions of one fundamental principle. 



188 THE LOGICAL BASES OF EDUCATION chap. 

§ 5. — We have seen that simple enumeration of 
instances in which certain phenomena occur together 
or in immediate succession to each other suggests a 
hypothesis of necessary connexion. The Method of 
Agreement attempts to confirm this hypothesis by 
varying, as much as possible, the circumsta,nces in 
which the relation is observed, so that all indifferent 
concomitants may be eliminated. If only one element 
is found constant under whatever conditions the 
phenomenon occurs that element is inferred to be 
probably the cause of the phenomenon. This is 
symbolized by the A — x of our formulae. For 
example, solids become liquids, and liquids change 
into gases, under all kinds of varying conditions, but 
one element, the presence of heat, is common to many 
of them. The inference is that heat is probably 
the cause of the change. Of course the evidence 
thus gathered is only sufficient to suggest this as a 
probable hypothesis ; a knowledge of the molecular 
structure of matter and of the action of both heat 
and pressure on molecular motion is necessary really to 
explain the phenomena, and this cannot be attained 
by any of the methods of direct induction we are 
now considering. 

The same limitation of the operation of the method 
is seen in an excellent example which we borrow from 
Professor Bain. " The north-east wind is known to be 
specially injurious to a great many persons. Let the 
enquiry be — what circumstances or quality is this owing 
to 1 By a mental analysis, we can distinguish various 
qualities in winds ; — the degree of violence, the tem- 
perature, the humidity or dryness, the electricity, 
and the ozone. We then refer to the actual instances 
to see if some one mode of any of these qualities 
uniformly accompanies this particular wind. Now 
we find, that as regards violence, easterly winds are 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 189 

generally feeble and steady, but on particular occa- 
sions, they are stormy ; hence, we cannot attribute 
their noxiousness to the intensity of the current. 
Again, while often cold, they are sometimes com- 
paratively warm ; and although they are more dis- 
agreeable when cold, yet they do not lose their 
character by being raised in temperature ; so that the 
bad feature is not coldness. Neither is there one 
uniform degree of moisture ; they are sometimes wet 
and sometimes dry. Again, as to electricity, there 
is no constant electric charge connected with them, 
either positive or negative, feeble or intense ; the 
electric tension of the atmosphere generally rises as 
the temperature falls. Farther, as regards ozone, 
they have undoubtedly less of this element than the 
south-west winds ; yet an easterly wind at the sea- 
shore has more ozone than a westerly wind in the 
heart of a town. It would thus appear that the 
depressing effect cannot be assigned to any one of 
these five circumstances. When, however, we 
investigate closely the conditions of the north- 
easterly current, we find that it blows from the pole 
towards the equator, and is for several thousand 
miles close upon the surface of the ground ; whereas 
the south-west wind coming from the equator descends 
upon us from a height. Now, in the course of this long 
contact with the ground, a great number of impure 
elements — gaseous effluvia, fine dust, microscopic 
germs — may be caught up and may remain suspended 
in the lower stratum breathed by us. On this point 
alone, so far as we can at present discover, the agree- 
ment is constant and uniform." ^ Here, it will be 
seen. Dr. Bain passes beyond the simple Method of 
Agreement both in appealing to the negative and con- 
trasted instance of the south-west wind, and in the 
^ Logic, vol. ii., p. 53. 



190 THE LOGICAL BASES OF EDUCATION chap. 

explanation of why passing near the ground should 
make a wind injurious. 

The Method of Agreement, then, can give us no 
more than an indication of the direction in which 
it would be well to push our enquiries. The degree 
of probability which we can attribute to the sug- 
gested hypothesis will depend upon the thoroughness 
with which all possible combinations of circumstances 
have been observed. It is in this variation of con- 
ditions that increase in the number of examples 
has value. Fifty examples of a sequence under the 
same conditions are of no more value than one, 
supposing that to have been observed correctly. 
But as we vary the instances we decrease the like- 
lihood that the phenomenon can have more than one 
' cause,' using the term in the half popular sense 
in which the methods employ it. 

But even invariable coincidence will not prove a 
causal relation. Day always follows night, and night 
succeeds to day, yet neither is the cause of the other. 
Both are joint effects of a deeper cause which the 
Method of Agreement cannot reach. Again, the 
invariable element may be a permanent fact in the 
universe, and in no causal relation to the phenomenon 
in question. As Mr. Hobhouse remarks : " Where- 
ever there is sea we find sky ; but we do not make 
sea the cause of sky, because we do not find the sky 
coming into being when or where the sea a.ppears. 
Conversely, fire is the cause of smoke, because the 
smoke comes out of the fire and disappears as the 
combustion ceases." ^ 

This leads us to see that without negative instances 

the inductive enquiry cannot advance either very far 

or very surely. The inference that increase of heat 

causes the change of solids into liquids and of liquids 

i The Theory of Knowledge, p. 367. 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 191 

into gases, gains in probability when it is shown that 
decrease of heat has the opposite effect ; and, as we 
saw. Dr. Bain finds in the negative instance of the 
south-west wind a confirmation of his hypothesis as 
to the reason of the noxiousness of the north-east 
wind. 

§ 6. — The Method of Agreement, then, must pass 
into the Method of Exclusions — or the Joint Method 
of Agreement and Difference, as Mill not very happily 
called it. Here the observation of positive instances 
is supplemented by the search for other instances, 
resembling the former as much as possible, with the 
one exception of the absence of both the supposed 
cause and effect. We constantly make inferences 
on the basis of this method in common life. " If a 
man finds that whenever he eats cucumber he 
suffers from indigestion, this indicates by Agreement 
that cucumber is the cause of his pain. But, if he 
is fond of cucumber, he will put the fault upon 
other ingredients of his diet taken at the same time, 
such as cheese, salmon, or pastry, which he likes less. 
Making, however, a second list of dinners (say) 
when visiting, at which cucumber is not served, 
whilst cheese, salmon, pastry, &c., all occur, and 
finding that he does not suffer from indigestion, the 
conclusion seems to be forced upon him that 
cucumber is the only pleasure of the table that must 
be bought with pain." ^ 

It was mainly by this method that Darwin estab- 
lished his theorj^ that vegetable mould is due to the 
action of earth-worms. He found that on lands of 
various kinds a layer of vegetable mould, continually 
increasing in thickness, is formed whenever earth- 
worms are present in any considerable numbers, so 
that objects left on the surface gradually become 

1 Carveth Read, Logic, Deductive and Inductive, p. 178. 



192 THE LOGICAL BASES OF EDUCATION ,chap. 

buried. On the other hand, where worms are 
practically absent, this phenomenon does not appear. 
Darwin used the method very thoroughly, and 
showed that what at first sight appeared to be 
exceptions were really negative instances. Large 
boulders were not buried, but investigation showed 
that under such boulders no earth-worms were to be 
found. 

It ajDpears from such examples that the negative 
instances are even more decisive than the positive, 
for they clear the ground of other possible alternative 
causes. 
Method of § 7. — An attempt to render the negative instance 
Difference. ^^ precise as possiblo is made by the Method oj 
Difference. The methods already considered have 
been methods of observation, but this is pre- 
eminently a method of experiment. Its aim is to 
vary, one at a time, the circumstances under which a 
phenomenon occurs. If, then, the supposed eifect is 
found to appear and disappear with the introduction 
and withdrawal of the supposed cause, the assump- 
tion of causal connexion is a strong one. The 
method is symbolized by the B — y and C — z of our 
formulae. 

It is obvious, however, that the method is 
emphatically one of testing and verification rather 
than of discovery j for unless we suspect a certain 
element to be the cause, why do we experiment with 
that rather than with any other of the concrete 
conditions ? 

It is very rarely that nature gives to observation 
such a perfect negative instance as the Method of 
Difference requires, and even in experiment it is 
extremely difficult to secure one. The surest plan is 
to introduce one new factor into a definitely knoAvn 
set of conditions. For example, as was accidentally 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 193 

discovered by Boyle in 1670, if an acid is introduced 
into an extract of litmus the colour is changed from 
blue to red, and the inference that the change is due 
to the acid is felt to be so safe that this change is 
the recognized test for the presence of an acid. But 
when, in experiment, we do attempt to make one 
definite change, it is often excessively difficult to 
avoid introducing at the same time other changes 
which are not intended and which may not even be 
suspected. Dr. Yenn gives a very instructive 
instance from the Report of the British Association, 
1881. "When Prof. G. H. Darwin and his brother 
were endeavouring to measure the lunar disturbance 
of gravity at the Cavendish Laboratory an extremely 
delicate pendulum was employed. So delicate was 
it that it almost defeated its purpose by registering 
innumerable minute disturbances, of which, whilst 
many could be accounted for, many others baffled all 
explanation. Amongst the former was this. In 
approaching the instrument in order to observe its 
reading, the surface level of the stone basement floor 
on which the instrument stood was deflected by the 
weight of the observer. Nay, as he stood to take a 
reading, the difference produced in this way by his 
merely shifting his weight from one leg to the other 
was perceptible ; so it became necessary always to 
observe the reading by a telescope from a distance, 
or to adopt some equivalent plan." ^ As Dr. Yenn 
goes on to observe, " Now of course exactly the same 
sort of disturbance is brought about whenever we have 
a letter weighed at the Post Office. But as it is not 
considered that the extra pence at stake are worth 
the trouble of deciding the weight of the letter to 
such a point of accuracy, we are content to let this 
source of inaccuracy enter, and therefore we use 
1 Empirical Logic, pp. 417 — 418. 

O 



194 THE LOGICAL BASES OF EDUCATION chap. 

instruments too coarse to indicate it when it does 
enter." ^ Such an example shows how difficult, if not 
impossible, it is to secure that only one circumstance 
is really varied at a time. 

Even supposing this difficulty overcome there still 
remains the probability that the new element intro- 
duced is not by itself the cause of the result. A 
lighted match is applied to a heap of gunpowder and 
an explosion follows, but the match by itself is not 
the cause of that explosion. And so it is generally. 
All that the Method of Difference can prove is that 
the introduction of a certain new element into a 
definite set of conditions is essential to the produc- 
tion of the effect in that case. But the cause ma}^ 
even lie wholly in some of the previous conditions, 
though held in check by others of those conditions, 
and all that the new element may do is to neutralize 
those interfering conditions and allow the causal 
connexion to have full plaj^ For example, if the 
string which supports a picture breaks, the inter- 
ference with the causal action of gravity is removed, 
but only in the most popular sense of the term can 
the breaking of the string be called the cause of the 
fall of the picture. - The Method of Difference alone 
will not, therefore, establish a pure case of causal 
connexion between the introduced element and the 
result. But when other evidence points to such a 
connexion, the confirmation afforded by this method 
is very strong, and in cases of ordinary experience, 
where scientific accuracy is not required, it may often 
be regarded as practically conclusive. Such cases 
are the most numerous in the affairs of every-day 
life. " Many precautions, for instance, which it 
would be ridiculous for a tradesman to adopt if he 
were weighing out a pound of sugar for a customer, 
^ Empirical Logic, pp. 417 — 418. 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 195 

are just the things which it would be little short of 
criminal for an analytical chemist not to adopt, if he 
were set to determine whether a given sample of 
water were pure. And precautions again which 
would suffice for this latter may again become in- 
sufficient when some original investigator is carrying 
out an excessively refined course of experiments in 
his laboratory. All accuracy in these matters is a 
question of degree, to be determined by the end we 
have in view, and strictly regulated by the necessities 
which the attainment of that end reasonably 
demands." ^ 

§ 8. — The evidence of causal connexion furnished Method of 
by a combination of affirmative and negative £Sf°"^^ 
instances is considerably strengthened when the Variations, 
facts can be brought under the Method oj Con- 
Gomitant Variations, the principle of which is that 
corresponding changes in the amount of phenomena 
give a presumption of causal connexion. By itself 
such variation is strong evidence of causal connexion 
only when the amount of the supposed cause can be 
changed at will and when the assumed effect varies in 
simple proportion with it. But if the supposed cause 
is not under control, so that the variations can only 
be observed, and not determined, by us, then there is 
always the possibility .that both the observed 
phenomena may be joint effects of an unknown 
cause. On the other hand, if the variations of the 
assumed cause and effect follow different laws it is 
evident that the full cause is not known. If, for 
example, in the sequence A — x, we have as varia- 
tions A, 2A, 3A, &c., and x, 4x, 9x, &c., then it 
would seem certain that A cannot be the whole 
cause of x. When the variations cannot be 

^ Venn, op. cit. p. 417. 

2 



196 THE LOGICAL BASES OF EDUCATION chap. 

measured, so that we can only observe that some 
change in x is connected with every change in A, the 
evidence is, of course, considerably weaker than when 
measurement is possible. It appears, then, that the 
mere fact of concomitant variation cannot, by itself, 
prove causal connexion. But when it is used to 
supplement the Method of Exclusions or that of 
Difference it considerably strengthens the evidence, 
even when measurement is impossible. 

To take an example from biology. Darwin 
advanced the hypothesis that flowers "have been 
rendered conspicuous in contrast with the green 
leaves, and in consequence at the same time beauti- 
ful, so that they may be easily observed by insects. 
I have come to this conclusion from finding it an 
invariable rule that when a flower is fertilized by 
the wind it never has a gaily-coloured corolla. 
Several plants habitually produce two kinds of 
flowers : one kind open and coloured so as to attract 
insects ; the other closed, not coloured, destitute of 
nectar, and never visited by insects."^ Here we 
have a hypothesis suggested by the Method of 
Exclusions. Further observations directed to the 
testing of this hypothesis have shown that the 
Method of Concomitant Variations is applicable. 
Thus Dr. Wallace writes : " The argument in favour 
of this view is now much stronger than when 
[Darwin] wrote ; for not only have we reason to 
believe that most of these wind-fertilized flowers are 
degraded forms of flowers which have once been 
insect-fertilized, but we have abundant evidence that 
whenever insect agency becomes comparatively in- 
effective, the colours of the flowers become less 
bright, their size and beauty diminish, till they are 
1 The Origin of Species, p. 16L 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 197 

reduced to such small, greenish, inconspicuous flowers 
as those of the rupture-wort . . . the knotgrass . . . 
or the cleistogamic flowers of the violet." •"■ 

Mr. Hobhouse gives an instructive example of a 
similar strengthening of the Method of Exclusions 
by that of Concomitant Variations. "Wealth is 
greatly increased by the change from production on 
the small to production on a large scale, by the intro- 
duction of machinery and the division of labour. 
This holds equally if we compare a railway with a 
stage-coach, or a coach with a pack-horse ; a cotton- 
mill with a spinning-wheel, or a spinning-wheel with 
a distaff and spindle. Under every form, at every 
stage and in every period, wealth has been increased 
by improved and extended co-operation between 
human beings. This complex co-operation of many- 
sided individual effort then appears as the main- 
spring of industrial progress. Where it is not we 
have stagnation — primitive barbarism ; where it is 
found, in whatever form or degree, there by one 
means and another industry is improved and the 
material side of life made perfect." ^ 

Especially valuable is the Method of Concomitant 
Variations when a really negative instance cannot 
be obtained, because the cause is a permanent factor 
throughout the universe. We cannot, for instance, 
get rid of either gravitation or temperature. 
But the latter can be varied at will between com- 
paratively wide limits and the effect of this variation 
on different phenomena noted, whilst even with the 
former such experimental variation is not out of the 
question. By ascending a high mountain or going 
up in a balloon, experiments can be made on the 
rate at which a body falls towards the earth, and by 

^ Darwinism, p. 332. 

•2 The Theory of Knowledge, p. 370. 



198 THE LOGICAL BASES OF EDUCATION chap. 

careful measurements this rate can be shown to 
decrease, continuously though gradually, as the 
height above the level of the sea increases. 

Such examples of the Method of Concomitant 
Variations show that in its most perfect application 
it becomes a method of establishing relations in a 
quantitative form. None of the other methods can 
determine quantitative relation between cause and 
effect, yet without such determination the statement 
of relations remains vague and indefinite. As 
Herschel says : " Numerical precision ... is the 
very soul of science . . . Indeed, it is a character 
of all the higher laws of nature to assume the 
forms of precise quantitative statement." ^ No doubt, 
measurement is never exact, though it becomes more 
so with the improvement of instruments. But by 
dealing with a series of measurements by averaging 
and other methods of statistics, a law is calculated 
which is more correct than any actual measurements. 
" The place of a planet at a given time is calculated 
by the law of gravitation ; if it is half a second wrong, 
the fault is in the instrument, the observer, the 
clock, or the law ; now, the more observations are 
made, the more of this fault is brought home to the 
instrument, the' observer, and the clock." ^ 

The form of the quantitative variation between 
two elements is often most clearly seen when it is 
represented graphically, as in the diagrams of 
the variations of the heights of the barometer and 
thermometer common in newspapers. A horizontal 
line, called the abscissa, represents the units of one 
element, and a perpendicular line, termed the ordi- 
nate, those of the other. " If the abscissae repre- 
sent intervals of time, and the ordinates correspond- 

^ Discourse on Natural Philosophy, §§ 115 — 116. 
■2 Clifford, Lectures and Essays, pp. 91 — 92. 



XIV DIRECT DEVELOPMENT OP HYrOTHESES 199 

ing heights of the barometer, we may construct curves 
which show at a glance the dependence of barometric 
pressure upon the time of day." ^ Curves constructed 
on the same principle are extremely valuable for 
exhibiting the variations in the growth of children 
with their age. The abscissae show the age 
divided into years or other convenient units of time, 
the ordinates, the various physical measurements, 
such as height, weight, and chest-girth. Tables 
thus constructed and showing the average of a large 
number of measurements make evident, for example, 
that, as compared with the average development of 
English children, the Lancashire half-timers show an 
arrest of development coincident in time with their 
beginning to work in the cotton-mills.^ 

When the Method of Concomitant Variations 
suggests a hypothesis, care must be taken to deter- 
mine the limits within which it is really applicable, 
by finding the negative instances which mark those 
limits. For example : "Water contracts as it is cooling. 
Suppose we begin to note this continued contracting 
of water from 100° F. to 90° ; we naturally expect to 
find it continuing through 90° to 80°. And as we 
observe, we find our expectations confirmed. And so 
on through to 40°, we find that water continues to 
contract. It is, therefore, most natural for us to 
expect to find water contracting at 39°. But just 
at this point in the series, there is a break in the 
continuity of variation ; at 39° water begins to 
expand and so continues until it passes into the 
solid form at the freezing point." ^ 

^ Thomson and Tait, Elements of Natural Philosophif, 
vol. i., p. 119. 

^ See the Tables given in Mr, Mark's Educational Theories 
in England, pp. 52 — 53. 

^ Hibben, Inductive Logic, pp. 142—143. 



200 THE LOGICAL BASES OF EDUCATION 



Method of 
Residues. 



§ 9. — Mill enunciated a fifth, method, that of 
Residues, whose principle is that when the known 
causes at work are not sufficient to account for the 
whole of the observed effect, the residual phenomenon 
presents a further problem for investigation. This 
is only a method by which hypotheses are suggested, 
and, as several instances of its working have already 
been mentioned, we need not consider it further.^ 

§ 10. — We will close this chapter by illustrating 
the employment of the various inductive methods in 
one and the same scientific enquiry, choosing as our 
example Dr. Wallace's account of the investigation 
into the origin of modifications of colour in animals. 
The existence of a problem is suggested not by mere 
variation of colour, which " would require no other 
explanation than does that of the sky or the ocean, 
of the ruby or the emerald — that is, it would require 
a purely physical explanation only."^ It is "the 
fact that the colours are localized in different pat- 
terns, sometimes in accordance with structural 
characters, sometimes altogether independent of them ; 
while often differing in the most striking and fantastic 
manner in allied species," which compels us " to look 
upon colour not merely as a physical but also as a 
biological characteristic."^ So far we have simple 
enumeration. Then the Method of Exclusions is 
employed to suggest a hypothesis. "As a rule, 
colour and marking are constant in each species of 
wild animal, while, in almost every domesticated 
animal, there arises great variability." ^ Then analogy 
is appealed to for a common characteristic, present 
uniformly in the one case and absent in the other, 
which may give the ground of this uniformity. " The 
essential difference between the conditions of life of 



Seep. 168. 
Ibid. 



^ Darwinism, p. 
^ Ihid., p. 189- 



189. 
190. 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 201 

domesticated and wild animals is, that the former 
are protected by man, while the latter have to pro- 
tect themselves." ^ Hence arises the hypothesis that 
the variations of colour in wild animals are of use to 
them in the maintenance of life. 

On proceding to test this hypothesis, " the fact 
that first strikes us in our examination of the colours 
of animals as a whole, is the close relation that exists 
between these colours and the general environment. 
Thus, white prevails among arctic animals ; yellow or 
brown in desert species ; while green is only a tropical 
colour in tropical evergreen forests." ^ Here the 
Method of Agreement suggests that the colour of the 
animals is related to that of their surroundings. 

Dr. Wallace then examines the case of arctic 
animals in more detail, and is able to appeal to the 
Method of Concomitant Variations in addition to that 
of Agreement. " In the arctic regions there are a 
number of animals which are wholly white all the 
year round, or which only turn white in winter. 
Among the former are the polar bear and the 
American polar hare, the snowy owl and the Green- 
land falcon ; among the latter the arctic fox, the 
arctic hare, the ermine, and the ptarmigan. Those 
which are permanently white remain among the 
snow nearly all the year round, while those which 
change their colour inhabit regions which are free 
from snow in summer." ^ This supports the 
hypothesis that the colouring is " protective, serving 
to conceal the herbivorous species from their 
enemies, and enabling carnivorous animals to 
approach their prey unperceived."* 

This, however, is not the only possible hypothesis. 
" Two other explanations have . . . been suggested. 
One is, that the prevalent white of the arctic regions 
1 Darwinism, p. 190. ^ /^^-^^^ 3 j^i^^^ 4 jj^i^^ 



202 THE LOGICAL BASES OF EDUCATION chap. 

has a direct effect in producing the white colour in 
animals, either by some photographic or chemical 
action on the skin or by a reflex action through 
vision. The other is, that the white colour is 
chiefly beneficial as a means of checking radiation 
and so preserving animal heat during the severity of 
an arctic winter. The first is part of the general 
theory that colour is the effect of coloured light on 
the objects — a pure hypothesis which has, I believe, 
no facts whatever to support it. The second 
suggestion is also an hypothesis merely, since it has 
not been proved by experiment that a white colour, 
'per se, independently of the fur or feathers which is 
so coloured, has any effect whatever in checking the 
radiation of low-grade heat like that of the animal 
body. But both alike are sufficiently disproved by 
the interesting exceptions to the rule of white color- 
ation in the arctic regions, which exceptions are, 
nevertheless, quite in harmony with the theory of 
protection." ^ 

These exceptions are, then, crucial instances 
which decide between the- rival hypotheses. Dr. 
Wallace examines several in detail and shows they 
are either not really exceptions to the rule of 
protective coloration or that the animals have no 
need of such protection. " The sable retains its 
rich brown fur throughout the Siberian winter ; but 
it frequents trees at that season and not only feeds 
partially on fruits or seeds, but is able to catch 
birds among the branches of the fir-trees, with the 
bark of which its colour assimilates." ^ 

The musk sheep is also brown, " but this animal 
is gregarious, and its safety depends on its associa- 
tion in small herds. It is, therefore, of more 
importance for it to be able to recognize its kind at 
^ Darwinism, pp. 190 — 19L ^ Ibid., p. 191. 



XIV DIRECT DEVELOPMENT OF HYPOTHESES 203 

a distance than to be concealed from its enemies . . . 
But the most striking example is that of the 
common raven, which is a true arctic bird, and is 
found even in mid-winter as far north as any known 
bird or mammal. Yet it always retains its black 
coat, and the reason, from our point of view, is 
obvious. The raven is a powerful bird and fears no 
enemy, while, being a carrion-feeder, it has no need 
for concealment in order to approach its prey." ^ 
These apparent exceptions are, therefore, brought 
under the Method of Exclusions and shown to be 
really negative instances. It is only :when this can 
be done that " exceptions prove the rule." 

Dr. Wallace then proceeds to show that the same 
principle applies throughout animal life. " In the 
desert regions of the earth we find an even more 
general accordance of colour with surroundings. . . . 
Passing on to the tropical regions, it is among their 
evergreen forests alone that we find whole groups of 
birds whose ground colour is green." ^ Nocturnal 
animals, fish, eggs, all furnish additional examples, 
and, in every case, apparent exceptions can be shown 
to be either not exceptions at all as their colour is 
adapted to their individual environment, or else to 
be really negative instances generally coming under 
the head of colour for recognition in the case of 
gregarious animals. 

Even such a brief and condensed outline as this 
of a piece of real scientific work will show the 
extreme difficulty of the task, the care with which 
every apparent exception must be investigated, 
and the importance for corroboration of negative 
instances. 

^ Darwinism, p. 191. ^ Ibid., p. 192. 



CHAPTER XV 



INDIRECT VERIFICATION OF HYPOTHESES 



Relation § 1. — The methods of direct inductive enquiry 

toDh-ec?^ which we considered in the last chapter are only 
Methods. applicable to simple cases in which the whole of the 
supposed causal sequence can be observed, and even 
in such cases they only form the first steps in an 
inductive enquiry. Their results are what are 
commonly called Um^nrical Laws, that is, laws of 
a descriptive character giving the results of sense- 
perception. They may state that an observed 
sequence is most likely causal, but they give no 
reason why it is so, for each law stands as an 
isolated fact, and is, therefore, unexplained. Such 
laws can never attain theoretical certainty, though 
they may have a high degree of probability. Certainty 
is only reached when we are able to show " not 
merely that that particular supposition will explain 
the facts, but also that no other one will." ^ In 
other words, we must exclude the possibility of 
alternative causes. But, as has been seen, this 
cannot be done so long as we keep to sequences 
open to sense-perception, for the causal relation is 
^ Clifford, Lectures and Lssays,'-p. 137. 



XV INDIRECT VERIFICATION OF HYPOTHESES 205 

often a hidden one. Even when we can use the 
inductive methods, therefore, we must still supple- 
ment them if we wish to attain to scientific precision 
and certainty. The only way to do this is to 
assume a hypothesis as to the hidden cause, to 
infer deductively the consequences of that hypothesis, 
and to compare those consequences with fact. 

Such a hypothesis is still suggested by facts under 
the guidance of analogy, but it does not, as it were, 
He on the face of the facts, and the suggestion is 
not a direct one. The facts have been already 
brought under empirical laws of considerable proba- 
bility before the attempt is made to organize those 
laws under wider and more certain generalizations. 
The empirical laws form the immediate material from 
which this deeper induction starts. It is obvious 
that in this higher work of science we have a task 
of infinitely greater difficulty, and requiring im- 
measurably greater knowledge, than any we have 
yet considered. The establishment of every such 
hypothesis marks indeed an epoch in the advance of 
knowledge. As examples, we may cite the theories 
of Gravitation and of Evolution, which revolutionized 
the physical and biological sciences. 

§ 2. — It is not, however, only in these higher initial Use 
realms of knowledge that the indirect method is the Method. 
only one available, and we shall first consider it in 
simpler cases. Whenever the whole causal sequence 
is not open to inspection, we are compelled to resort 
to it. If we are given an effect and have to find 
its cause, the only method available is to assume a 
cause hypothetically, deduce its consequences, and 
see if they agree with the facts. A single real 
exception is fatal, but, as we saw in the last chapter, 
many facts which at first sight seem to be exceptions, 
turn out upon deeper investigation to be really 



206 THE LOGICAL BASES OF EDUCATION chap. 

negative instances by which the hypothesis is con- 
firmed. 
Circum- In the ordinary affairs of life we are contented 

Evidence, with hypotheses which fairly cover the facts, without 
demanding proof that they do so exactly, or that no 
other supposition will do so. We cannot wait in 
practice for theoretical certainty. Even in the law- 
courts, if the facts adduced make strongly against 
an accused person, the prisoner must either establish 
other facts incompatible with his guilt, or take the 
consequences. Especially is this so in cases of 'circum- 
stantial evidence,' in which the concurrence of many 
facts, each in itself perhaps of no great importance, 
often gives a presumption of very strong probability 
in favour of a certain hypothesis. As Mr. Hobhouse 
says : "A man is found dead with his throat cut. 
A knife is found in a ditch close by. There are 
footprints in the mud. X was known to be in the 
neighbourhood on the day ; evidence is given that 
he purchased the knife a week before ; his. boots fit 
the footprints. All tiiese facts might be due to a 
collocation of separate causes, but all are explicable 
by a single cause, namely, that X planned and 
. carried out the murder. The single assumption is 
so much more probable than the multiple com- 
bination of circumstances that it is likely to go hard 
with X, and his business is to produce some fact in- 
compatible with the above explanation. Failing this, 
one or two more such combinations of circumstances 
and our conviction of the strength of the hypo- 
thetical argument will be evinced in a very practical 
manner.' ^ But, even at the best, the conclusion is 
only a probable one, and, undoubtedly, many an 
innocent man has fallen a victim to an unfortunate 
conjunction of circumstances. The danger in every 
^ The Theory of Knowledge, p. 422. 



XV INDIRECT VERIFICATION OF HYPOTHESES 207 

case of circumstantial evidence is that facts 
really pertinent to the question in hand may be 
overlooked, or neglected as immaterial. Especially 
is this apt to occur when the observer is biased 
in favour of a hypothesis, perhaps hastily formed. 
There are always some facts inconsistent with a 
false hypothesis if only they could be found. 

§ 3. — In history the indirect method of establishing The in- 
hypotheses is the only one available, and the same Method in 
applies to a great extent in all branches of social History. 
science. Owing to the extreme complexity of the 
subject-matter, dealing as it does with all the motives 
and circumstances which can influence human conduct, 
it is impossible to apply the direct inductive methods, 
for the phenomena cannot be isolated for examina- 
tion, even in the present. Moreover, history suffers 
from the exceptional initial difiiculty of having to 
rely upon testimony, often of an inferior character, 
for its facts. Thus, throughout, " History is not . . . 
a science of observation, but a science of reasoning. 
In order to use facts which have been observed under 
unknown conditions, it is necessary to apply criticism 
to them, and criticism consists in a series of reason- 
ings by analogy. The facts as furnished by criticism 
are isolated and scattered ; in order to organize them 
into a structure it is necessary to imagine and group 
them in accordance with their resemblances to facts 
of the present day, an operation which also depends 
on the use of analogies ... In order to frame its 
arguments from analogy, it must combine the know- 
ledge of the particular conditions under which the 
facts of the past occurred with an understanding of 
the general conditions under which the facts of 
humanity occur." ^ 

^ Langlois and Seignobos, Introduction to the Study of 
History, p. 317. 



208 THE LOGICAL BASES OF EDUCATION chap. 

In pursuing such a method two opposite dangers 
present themselves. On the one hand is the danger 
of making history a mass of mere empirical facts 
with no generalizations to bind them together ; on 
the other, that of inferring consequences from 
abstract principles gathered from an analysis of 
general human nature, and advancing these as true 
without bringing them to the test of comparison 
with actual facts. It is the tendency to fall into 
this last error which has brought such subjects as 
the philosophy of history and the science of political 
economy into some disrepute. But to assume that 
such branches of knowledge are valueless because 
some of their exponents have adopted too abstract a 
treatment is to fall into the opposite error. The 
subject of education presents another example. On 
the one hand we have the ' practical ' teacher who 
despises ' theory ' and values only the facts of his 
own experience. On the other, we have the arm- 
chair ' theorist ' who deduces laws from the general 
principles of logic and psychology, or even from such 
a vague conception as Rousseau's ' Nature,' and 
advances them as rules to be put into practice 
irrespective of circumstances. The wise educator 
stands between the two. 
The In- § 4. — Sciences such as geology and biology, which 

Method in attempt to explain the origin of the present from the 
BioiofJ.^^^ evidence of the material traces left by the past, must 
continually resort to the indirect method. In such 
investigations the inductive methods considered in 
the last chapter are applicable mainly in the verifi- 
cation of consequences deduced from hypotheses 
which go behind the facts in attempting to explain 
them. 

We will borrow for analysis a typical example 
from geology. In the account of the glacial phe- 



XV INDIRECT VERIFICATION OF HYPOTHESES 209 

nomena of the British Isles contributed by my 
colleague, Mr. P. Kendall, to Professor Wright's 
Mail and the Glacial Period^ we read : " From the 
neighbourhood of Lichfield, through some of the 
suburbs of Birmingham, and over Frankley Hill and 
the Lickey Hills to Bromsgrove, there is a great 
accumulation of Welsh erratics, from the neighbour- 
hood, probably, of Arenig Mawr." ^ The problem 
is to account for the transportation of these boulders 
some sixty or seventy miles from their source. 

Two hypotheses were advanced ; one that they 
had been borne by marine ice during a period when 
the land was submerged, the other that they had been 
transported by glaciers. The consequences of each 
of these hypotheses must be deductively inferred and 
then tested by comparison with the facts. 

Mr. Kendall first explains exactly what the 
glacial hypothesis involves. " During the early 
stages of the Glacial period the Welsh ice had the 
whole of the Severn Valley at its mercy, and a great 
glacier was thrust down from Arenig, or some other 
point in central Wales, having an initial direction, 
broadly speaking, from west to east. This glacier 
extended across the valley of the Severn, sweeping 
past the Wrekin, whence it carried blocks of the 
very characteristic rocks to be lodged as boulders 
near Lichfield ; and it probably formed its terminal 
moraine [in that neighbourhood]. As the ice in the 
north gathered volume it produced the great Irish 
Sea Glacier, which pressed inland and down the 
Vale of Severn ... and brushed the relatively small 
Welsh stream out of its path, and laid down its own 
terminal moraine in the space between the Welsh 
border and the Lickey Hills." ^ Of course such a 
hypothesis is based on many traces left in the forma- 
1 Op. cit., p. 150. 2 Qr^ ciY., p. 151. 

p 



210 THE LOGICAL BASES OF EDUCATION chap. 

tion of the land, the force of which would only be 
felt by a geologist. It grows out of the facts open to 
observation, though it goes much beyond them in its 
mental construction of a s^et of conditions so diiferent 
from the present state of things. 

Mr. Kendall then proceeds to examine the evidence 
in detail, comparing it at each step with the conse- 
quences which can be inferred both from the hypo- 
thesis of glacial agency and from that of the action 
of marine ice. Each group of facts is thus made 
a crucial instance and shown at once to support 
the former supposition and to conflict with the 
latter. 

The first step is to dispose of apparent exceptions 
by showing that on analysis they really negate the 
hypothesis they appear at first sight to support, and 
confirm that with which they seem on a casual view to 
be in conflict. " Within the area in England and 
Wales covered by the Irish Sea Glacier all the 
phenomena point to the action of land-ice, with the 
inevitable concomitants of sub-glacial streams, extra 
morainic lakes, &c. There is nothing to suggest 
marine conditions in any form except the occurrence 
of shells or shell fragments ; and these present so 
many features of association, condition, and position 
inconsistent with what we should be led to expect 
from a study of recent marine life, that concholo- 
gists are unanimous in declaring that not one single 
group of them is on the site whereon the shells lived. 
It is a most significant fact — one out of a hundred 
which could be cited did space permit — that in the 
ten thousand square miles of, as it is supposed, 
recently elevated sea-bottom, not a single example 
of a bivalve shell with its valves in apposition has 
ever been found ! Nor has a boulder or other stone 
been found encrusted with those ubiquitous marine 



XV INDIRECT VERIFICATION OF HYPOTHESES 211 

parasites, the barnacles." ^ Thus, when the presence 
of sea shells is analysed, the mode of that presence 
is seen to be inconsistent with the hypothesis of 
marine-ice, which the bare unanalysed fact of their 
presence seemed at first sight to support. On the 
other hand, though this presence of shells is not a 
direct consequence which can be inferred from the 
hypothesis of land-ice, yet it is not inconsistent with 
that supposition. For this hypothesis assumes the 
existence of the Irish Sea prior to its invasion by 
the glacier. When this invasion took place the 
glacier would be likely to sweep up shells from the 
shell-banks on the sea-floor. Mr. Kendall tells me 
that when he advanced this explanation it was 
unsupported by any observed case of actual shell- 
transportation by glaciers, but that in 1897, several 
years after the albove was written, a glacier thus carry- 
ing shells was discovered in Spitsbergen. This may be 
said practically to complete the evidence required 
on the point. 

Having disposed of the apparent disagreement 
between the theory of land-ice and the facts, Mr. 
Kendall proceeds to summarize the positive evidence, 
and to show that this evidence negates the marine- 
ice supposition. " The evidences of the action of 
land-ice within the area are everywhere apparent in 
the constancy of direction of — (1) Striae upon rock 
surfaces. (2) The terminal curvature of rocks. (3) 
The ' pull-over ' of soft rocks. (4) The transportal 
of local boulders. (5) The orientation of the long 
axes of large boulders. (6) The false bedding of 
sands and gravels. (7) The elongation of drift-hills. 
(8) The relations of 'crag and tail.' There is a 
similar general constancy, too, in the directions of 
the striae upon large boulders. Upon the under side 
1 Op. ciL, pp. 151—152. 

P % 



212 THE LOGICAL BASES OF EDUCATION chap. 

they run longitudinally from south-east (or there- 
abouts) to north-west, while upon the upper surface 
they originate at the opposite end, showing that the 
scratches on the under side were produced by the 
stone being dragged from north-west to south-east, 
while those on the top were the product of the pas- 
sage of stone-laden ice over it in the same direction. 

" Such an agreement cannot be fortuitous, but 
must be attributed to the operation of some agent 
acting in close parallelism over the whole area. To 
attribute such regularity to the action of marine 
currents is to ignore the most elementary principles 
of marine hydrology. Icebergs must, in the, nature 
of things, be the most erratic of all agents, for the 
direction of drift is determined, among other vary- 
ing factors, by the draught of the berg. A mass of 
small draught will be carried by surface currents, 
while one of greater depth v/ill be brought within 
the influence of under-currents ; and hence it not 
infrequently happens that while floe -ice is drifting, 
say, to the south-east, giant bergs will go crashing 
through it to the north-west. There are tidal in- 
fluences also to be reckoned with, and it is matter of 
common knowledge that flotsam and jetsam travel 
back and forth, as they are alternately affected by 
ebb and flood tide. 

"Bearing these facts in mind, it is surely too 
much to expect that marine ice should transport 
large boulders (how it picked up many of them also 
requires explanation) with such unfailing regularity 
that it can be said without challenge, ' Boulders in 
this district [South Lancashire and Cheshire] never 
occur to the north or west of the parent rock.' The 
same rule applies without a single authentic excep- 
tion to the whole area covered by the eastern branch 
of the Irish Sea Glacier ; and hence it comes about 



XV INDIRECT VERIFICATION OF HYPOTHESES 213 

that not a single boulder of Welsh rock has ever 
been recorded from Lancashire." ^ 

Throughout this example we see the attempt to 
establish the hypothesis, not only by showing that 
it will explain the facts, but by proving that the 
only other possible supposition fails to do so. 

§ 5. — Passing now to the establishment of those Establish- 
wider truths to which we referred at the beginning Theory of 
of this chapter, we will take as our example the Gravitation: 
development of the Theory of Gravitation. 

The idea that material bodies attract each other Empirical 
had been familiar to the ancient Greek philosophers, paTung 
but it only became useful to science when it was -^<"^^«s- 
made definite by measurement. The first step was 
taken by Galileo in the first half of the seventeenth 
century. From the consideration of a great number 
of facts he was led to the hypothesis that all bodies 
fall with equal rapidity under the attraction of the 
earth, independently of both their size and their 
material. By letting various bodies fall at the same 
moment from the top of the leaning tower of Pisa 
he gave an approximate verification of this hypothesis, 
attributing the trifling differences in the times they 
took to reach the ground to the greater resistance 
offered by the air to light than to heavy bodies. 

Newton succeeded in making the verification much 
more exact " by the simple and elegant contrivance 
of enclosing in a hollow pendulum the same weights 
of a great number of substances the most different 
that could be found in all respects, as gold, glass, 
wood, water, wheat, &c., and ascertaining the time 
required for the pendulum so charged to make a 
great number of oscillations ; in each of which it 
is clear the weights had to fall, and be raised again 
successively, without loss of time, through the same 
1 Op. cit., pp. 152—153, 



214 THE LOGICAL BASES OF EDUCATION chap. 

identical spaces. Thus any difference, however in- 
considerable, that might exist in the time of one such 
fall and rise would be multiplied and accumulated 
till they became sensible. And none having been 
discovered by so delicate a process in any case, the 
law was considered verified both in respect of gener- 
ality and exactness." ^ Here, as Newton was study- 
ing one force only, he maintained all other conditions 
— such as the resistance of the air- — constant by the 
simple device of using the same pendulum. 

Galileo had also advanced the hypothesis that the 
spaces described by falling bodies must vary as the 
squares of the times, and he based this on the sup- 
position that this was the simplest law that could be 
assigned. This argument, of course, was somewhat 
insecure, but the truth of the hypothesis was approxi- 
mately verified by experiment. 
Empirical Nearly forty years before Galileo's enunciation 
of the laws of falling bodies Kepler had entered upon 
his memorable investigations into the motions of the 
planets. The current theory was that each planet 
revolved round the sun in a circular path, and it was 
only after the failure of many attempts to reconcile 
the observed positions of the planets with this theory, 
by moving the centres of the circles in all kinds of 
ways away from and towards the sun, that Kepler 
at last hit on the true hypothesis of an elliptical 
orbit. The final outcome of his researches was the 
enunciation of the three laws still known by his 
name — that each planet revolves round the sun in an 
elliptical path, having the sun in one of the foci ; 
that it revolves with such a velocity that a straight 
line drawn from it to the sun passes over equal 
areas in equal times ; and that the squares of the 
number of days taken by the planets to complete a 
^ Herschel, Discourse on Natural Philosophy, § 179. 



Laws of 

Planetary 

Motion. 



XV INDIRECT VERIFICATION OF HYPOTHESES 215 

revolution are proportional to the cubes of their 
mean distances from the sun. 

As established by Kepler these were merely 
empirical laws, descriptive of observed facts. "The 
laws as they came from Kepler's hands stood out as 
three independent truths ; thoroughly established 
but wholly unsupported by any explanations as to 
why these movements, rather than any other move- 
ments, should be those appropriate for the revolutions 
of the planets." ^ 

It was the great achievement of Newton to 
combine these empirical laws with those of falling 
bodies, and from the combination to conceive the 
famous theory of universal gravitation, in which they 
all found their explanation. " Newton's grand dis- 
covery bound together the three isolated laws of 
Kepler into one beautiful doctrine. He showed not 
only that those laws are true, but he showed why 
they must be true, and why no other laws could have 
been true." ^ 

This theory was not, however, reached all at once. GravUatior 
Newton first guessed that the force of gravity might Moon. *^ 
extend to the moon, and retain it in its orbit. 
Immediately, he proceeded to deduce by mathematical 
reasoning the results of this hypothesis, assuming 
that the empirical law of the square of the distance 
held true between earth and moon. Working with 
the reputed distance of the moon from the earth, he 
calculated that gravity should draw it towards the 
earth through more than fifteen feet every minute. 
But " according to Newton's calculations, made at 
this time, the moon, by her motion in her orbit, was 
deflected from the tangent every minute through a 
space of thirteen feet. . . . The difference seems 
small, the approximation encouraging, the theory 
1 Ball, Story of the Heavens, p. 117. ^ Ibid. 



216 THE LOGICAL BASES OF EDUCATION chap. 



plausible ; a man in love with his own fancies would 
readily have discovered or invented some probable 
cause of this dijfference. But Newton acquiesced in 
it as a disproof of his conjecture, and ' laid aside at 
that time any further thoughts of this matter.' " ^ 
Some fifteen or sixteen years after, Newton found " he 
had been mistaken in the magnitude of the earth, 
and consequently in the distance of the moon, which 
is determined by measurements of which the earth's 
radius is the base."^ He repeated his calculations, 
and his former supposition was now found to agree 
with the phenomena with remarkable precision. The 
law of gravitation was thus proved to apply to the 
moon. 

To conceive that the same law would explain the 
motions of the planets round the sun was a natural 
development. Indeed, that the different planets are 
attracted to the sun by a force which varies inversely 
as the square of the distance was already known to 
be approximately true. Newton, however, starting 
with the facts of planetary motion as expressed in 
Kepler's laws, showed by rigorous mathematical 
reasoning that these laws imply the law of gravita- 
tion as their ground, and are a necessary consequence 
of that law. 

Difficult and intricate as was the mathematical 
reasoning involved in this further verification of the 
theory of gravitation, the next step was more com- 
plicated still. It was to conceive gravity as a mutual 
attraction of all the members of the solar system. 

If this were true, then the moon, being attracted 
by the sun as well as by the earth, would move 
sometimes faster and sometimes more slowly than if 
attracted by the earth alone. Further, the same 

^ Whewell, History of the Inductive Sciences, vol. ii., p. 122. 
2 Ibid,, p. 123. 



XV INDIRECT VERIFICATION OF HYPOTHESES 217 

result would hold with the satellites of the other 
planets ; and if the planets attract each other, their 
movements would also show divergencies from those 
that would be due to the single attractive power of 
the sun. Here, then, were a set of deviations, small 
indeed in quantity, but excessively complicated in 
their nature. Newton worked out by a wonderful 
course of geometrical reasoning, all the chief per- 
turbations in the case of the moon, and indicated 
how a similar train of inference could be applied 
to the other satellites. When his results, thus 
deductively attained, were compared with the 
observations of Flamsteed, they were found to be 
surprisingly accurate. 

The final step in the development of the theory Gravitation 

€Xt€7lci€(Z 

of gravitation was taken when it was made ap- to aii 
plicable to all particles of matter, and not simply o/Matfer. 
to those concrete bodies of sensuous perception to 
which it had hitherto been applied. Of this sup- 
position, too, Newton proceeded to calculate the 
results, and he applied his reasonings to explain 
" the figure of the earth, the tides, the precession of 
the equinoxes, the regression of the nodes of a 
ring such as Saturn's, and of some effects which, at 
that time, had not been ascertained even as facts of 
observation ; for instance, the difference of gravity 
in different latitudes, and the nutation of the earth's 
axis. It is true, that in most of these cases, 
Newton's process could be considered only as a 
rude approximation. . . . Nevertheless the form and 
nature of the conclusions which [he] did obtain, 
were such as to inspire a strong confidence in the 
competency of his theory to explain all such 
phenomena as have been spoken of." ^ 

In all essentials, then, this magnificent discovery 
^ Whewell, op, cit., vol. ii., p. 135. 



218 THE LOGICAL BASES OF EDUCATION chap. 

— certainly one of the greatest ever made — was the 
work of one mighty intellect. By it, as Whewell 
remarks, " Astronomy passed at once from its boy- 
hood to mature manhood." -^ The task of subsequent 
astronomers has been only to work out the results 
of the theory in more detail and with more perfect 
accuracy. The scope of the principle has been con- 
tinually extended, till, as Sir Robert Ball tells us, 
"when we extend our view beyond the limits of 
our Solar System to the beautiful starry systems 
scattered through space we find even there evidence 
of the great law of universal gravitation." ^ 

Even the rough and meagre outline we have been 
able to give of the process of this great induction 
brings out clearly how small a part in it was played 
by direct inductions from sense-experience. Beyond 
the empirical laws of falling bodies and of the 
movements of the planets such inductions could not 
go. All the later steps were taken by the indirect 
method we are considering in this chapter ; and 
these steps could have been possible only to one who 
possessed enormous mathematical knowledge and 
capacity. "It was the extraordinary power with 
which Newton traced out geometrically the con- 
sequences of his theory, and submitted them to re- 
peated comparison with experience, which constitutes 
his pre-eminence over all physicists." ^ 

It must be noted that the theory goes far beyond 
sense-experience. " The law asserts that every 
particle of matter in the universe attracts every 
other particle, with a force depending on the masses 
of the particles and their distances. We cannot 
know the force acting on any particle unless we 

^ Whewell, op. cit., vol. ii., p. 137. 
• 2 Op^ cit., p. 122. 

^ Jevons, The Principles of Science, p. 556, 



XV INDIRECT VERIFICATION OF HYPOTHESES 219 

know the masses and distances and positions of all 
other particles in the universe." ^ Of course, such 
knowledge is unattainable, and our verifications of 
the law can, therefore, never be more than partial 
and approximate. But as man's powers of exact 
computation and precise observation are increased, 
the verifications become more and more exact, and 
in astronomy especially they have attained a truly 
wonderful degree of precision. We are, therefore, 
justified in believing the law of gravitation to be 
exactly true. In other words, our knowledge is more 
exact than our actual observations can ever be. 

Lastly, the law goes beyond sense-perception in 
that it not only describes, but explains phenomena. 
As we saw, Kepler's laws were merely descriptive ; 
they brought all possible observations of a planet's 
positions under general formulae. But the theory 
of gravitation is a causal law, explaining those 
motions by showing them as the necessary con- 
sequences of mechanical principles. Thus, the 
theory emphasizes the doctrine that knowledge is a 
mental construction suggested by observed facts, 
and continually verified by appeal to them, but not 
confined to the products of sense-perception. 

1 Jevons, The Principles of Science, p. 458 — 459. 



CHAPTER XVI 

DEFINITION, CLASSIFICATION, AND EXPLANATION 

§ 1. — To know is to be able to explain. The 
aim, therefore, of all the methods of developing 
knowledge which we have considered is the explana- 
tion of the experiences of humanity. That goal is 
far from being reached, but it is one towards which 
mankind has been, on the whole, continuously 
progressing. The ideal of explanation is to show 
both the place and the function in the system of the 
universe of that which is to be explained. This 
implies a knowledge both of the nature of the 
phenomenon in question and of its relations to other 
phenomena. Thus we see that the stage of ex- 
planation by system takes up into itself the two 
preceding stages of interpretation of the world which 
we considered in the first two chapters. 

We saw, further, in chapter v, that to each stage 
of interpretation there broadly corresponds a suitable 
form of judgment. The nature of things is most 
appropriately expressed in the categorical judg- 
ment, their relations to other things in the hypo- 
thetical judgment, and their union into system in 
the disjunctive judgment, which takes up the other 
two forms into itself. 



CH. XVI DEFINITION AND CLASSIFICATION 221 

Lastly, our examination of the inductive methods • 
of obtaining knowledge from a direct study of the 
world has made it clear that the same enquiry which 
aims at establishing the existence of universal law 
must also bring to light the nature of the things 
related. It is evident that the precision which can 
be given to a judgment of the form " If S is M it is P " 
is directly dependent on the exactness of our know- 
ledge of the nature of S, M, and P. 

Our attention has, however, been mainly concen- 
trated hitherto on the establishment of laws ; we 
must now examine the mutually involved processes 
of definition and classification. 

§ 2. — Like all attempts at organizing knowledge, Deveiop- 
classification and definition have their roots in the clfinit/on 
previously unorganized experiences of humanity. 
" Ages before the logician, or any one else who deals 
with systems, had a hand in the matter, the neces- 
sities of common life had been at work prompting 
men to group the things which they observed. All 
names imply the recognition of groups, and a great 
number of names imply a subordination of groups, 
so that at the earliest stage to which we can transfer 
ourselves we find that we are already in possession 
of a rudimentary classification ; and that we cannot 
even talk or think about the things without an 
appeal to this." ^ Of course, every such grouping 
was based on the recognition of common qualities, and 
the name implied that these qualities were present in 
any case in which it was applied. The rudimentary 
classification consequently involved a rudimentary 
definition, for definition is merely the statement of 
the common qualities which determine the classifi- 
cation. 

But, as was shown in chapter iii, words vary in 
^ Venn, Empirical Logic, p. 322. . 



222 THE LOGICAL BASES OF EDUCATION chap. 

their import according to the context in which 
they occur. For long ages, men did not attempt to 
make explicit the common element in these numerous 
occasional meanings, with the natural result of a 
want of precision in thought, which became more 
and more pronounced as both life and thought 
became more complex. Socrates was the first who 
began to enquire systematically what general mean- 
ing could be found as a constant element in all the 
specific meanings of words as used in actual speech. 
He enquired, as Xenophon tells us, into " what was 
pious, what impious ; what honourable, what base ; 
what sobriety, what excess ; what courage, what 
cowardice ; what a state, what a statesman ; what 
the government of men, what one who was capable 
of governing them. And so too on other subjects, 
the knowledge of which he thought rendered men 
honourable and good, but ignorance of them fit only 
to be designated as no better than slaves." ^ 

The method of Socrates in these enquiries, as it is 
shown us in the writings of Plato and Xenophon, 
was, in all essentials, the method by which modern 
science investigates the nature of reality. It was to 
examine different cases in which a term was applied, 
and by comparing them with cases in which the 
contrasted term was used, to try to determine what 
was the essence of the idea of which each word was 
a symbol. Nor was this — or is it ever — a question 
of mere words. For, as all the meaning of a word 
must be justified by the reality to which it refers, a 
determination of meaning is a determination of facts 
of reality. A verbal element dissociated from any 
meaning is, indeed, not a word at all. If a native 
of China were to address me in his native tongue, 
the sounds he uttered would be words to him, but 
1 Memorabilia, Bk. I., c. i. 



XVI DEFINITION AND CLASSIFICATION 223 

not to me. True learning of words is, then, true 
learning about facts ; and, as has been already said, 
there can be no learning of facts without words, or 
at any rate, without some kind of language-signs. ■•■ 

The aim, then, of such enquiries as those of 
Socrates is to discover what common nature exists 
in certain facts to justify the marking of them by 
the same word. The expression of such a common 
nature is a statement of the general meaning of the 
word, and this meaning, regarded as a mental fact, is 
called a conce'pt. All ideas corresponding to words 
are of the nature of concepts, for they are all, to some 
extent, a grasp of meaning. But the term ' concept,' 
when used strictly, implies a meaning or idea which 
is precise and accurate, and such a concept can only 
be attained by a careful process of analysis of reality, 
such as Socrates began, and which we can carry out 
much more accurately, and apply to a much greater 
range of reality, by the aid of the inductive methods. 
The final outcome of such a process is definition. 

§ 3. — Definition, then, is an expression of general Nature of 
meaning. It does not, however, necessarily include 
all that general meaning. The aim of definition is 
to be as brief as possible, consistently with precise 
accuracy. But any analysis of the common nature 
of things which is pushed very far shows that 
common qualities are in certain cases so connected 
together that some can be derived from others. For 
example, amongst the qualities common to all right- 
angled triangles are those of being inscribable in a 
semi-circle, and of having the square on the hypo- 
tenuse equal in area to the sum of the squares on 
the sides. But both these characteristics, as well as 
many others, can be deductively inferred from the 
fact that the triangle is right-angled. These derived 
1 Cf. pp. 45—46. 



Definition, 



224 THE LOGICAL BASES OF EDUCATION chap. 

qualities, which are technically called Properties, are, 
then, not expressed in the definition, because they are 
implied by stating in it the characteristic of having 
a right-angle. Similarly, such properties as being able 
to invent tools and generally to adapt his material 
environment more or less perfectly to his own needs, 
to study various branches of knowledge, to write 
poetry, paint pictures, establish systems of govern- 
ment, etc., are all properties of man inferrible from 
his possession of a rational will, and, therefore, would 
not be included in the definition. 

Again, there are sometimes other qualities which 
are common to a whole class, which we yet do 
not consider essential to the nature of that olass. 
Were they absent in any case we should still apply 
the name, so long as what we consider the more 
fundamental qualities were present. Thus, all swans 
known before the discovery of Australia were white, 
but when birds essentially similar in structure and 
mode of life, though black in colour, were found, no 
hesitation was felt in including them in the class 
swans. Such qualities are called Accidental Qualities 
or Accidents. It is evident that every individual 
thing has also many such accidental qualities ; in man 
we call them 'personal peculiarities.' 

In some cases, as in those just taken as 
examples, it is easy to see which are the derived, 
and which the more fundamental qualities. But not 
infrequently, especially in mathematics, this is a 
matter of arbitrary choice. Eor example, the equality 
of sides and of angles in an equilateral triangle are 
inferrible from each other. Which of these qualities 
we include in the definition, and which we conse- 
quently relegate to the rank of a property, is purely 
a matter of choice. Outside mathematics it is in 
many cases impossible, at any rate with our present 



XVI DEFINITION AND CLASSIFICATION 225 

amount of knowledge, to trace any such necessary- 
connexion at all. 

It follows, then, that a definition states a more 
or less arbitrarily chosen group of attributes, which 
form what is technically called the connotation of the 
word. It enunciates what we esteem the most 
important qualities. But importance is always 
relative to some purpose or theory. Hence, " a 
new principle or theory will often effect a complete 
change in the order of dependence or importance in 
which the attributes are regarded." ^ Many examples 
occur in the history of mathematics, but the most 
interesting to the general reader is the revolu- 
tion in this respect introduced into the biological 
sciences by the theory of evolution. "It is not so 
much that we have discovered new facts about the 
plants and animals as that a new theory has com- 
pletely altered the relative importance of the facts 
that were already known. " ^ 

Our definitions, then, cannot claim finality. Any 
new development in knowledge may lead to a profound 
modification of many definitions. Thus, with scien- 
tific terms, as Dr. Venn says, "their growth is 
their life." ^ Every change of definition is accepted 
only after a vast amount of careful and critical 
research, and, therefore, implies an advance in know- 
ledge, either of the facts involved or of the theory 
which unites them and gives them a meaning. 

With the words of ordinary language greater sta- 
bility is desirable, for words used by a whole nation 
must change their meaning, and consequently their 
application, but slowly, if at all, or communication by 
language would become increasingly difficult, espe- 
cially between one generation and another, if, indeed, 

1 Venn, op. cit., p. 284. '^ Ihid., pp. 285—286. 

3 Ibid., p. 288. 



226 THE LOGICAL BASES OF EDUCATION 



Definition 
and other 
Modes of 
stating 
Meaning. 



it did not become impossible. Of course, meamn^ 
do change in every living language, and travellei 
amongst savage tribes with a purely oral language 
tell us that this change is so rapid that in the course 
of a very few years what is practically a new language 
has developed. The reduction of language to writ- 
ing, the diffusion of books made possible by printing, 
and the general ability to read them, do much to 
increase the stability of a language. During the 
last three centuries, for example, many words have 
changed somewhat in meaning, as is evident from a 
comparison of Shakespeare and of the Authorized 
Version of the Bible with current usage But the 
change has been comparatively small, and we have 
no difficulty in understanding Elizabethan writers. 
Thus, the treasures of the past are open to us in a 
way they could not be did language change rapidly. 

I 4, — Again, as every definition states a more or 
less arbitrarily chosen group of common attributes, it 
is evident that it is only one way of stating meaning. 
But it is the most precise way, for it expresses just | 
what the most competent authorities regard as the , 
meaning of the word ; in other words, it expresses the ' 
value of the term in the existing body of knowledge. 
Definition is, therefore, not a question of individual 
choice and caprice, but of established usage, and the 
final appeal must be to those who are most competent 
by knowledge to determine that usage. This is re- 
cognized in science, and the whole essence of scien- 
tific language is the exactness and precision with 
which it uses its terms. With ordinary speech there 
is much less precision, simply because it expresses 
much less exact thought. "As long as popular 
thought is vague its language must be vague ; nor is 
it desirable too strictly to correct the language whilst 
the thought is incorrigible. Much of the effect of 



XVI DEFINITION AND CLASSIFICATION 227 

poetry and eloquence depends upon the elasticity and 
indirect suggestiveness of common terms." ^ 

But this want of precision in language is a fruitful 
source of misunderstanding and of confusion of 
thought, and it is obvious that it must be confined 
within recognized, if not very precise, limits. In 
other words, whatever else a word may imply in any 
particular passage it must at least be held to imply a 
fixed nucleus of general meaning. The statement of 
this is the definition. This may not be explicitly 
present to the mind of either the user or the receiver 
of the word, but it must be held to be implied, and 
if the word is used with a correct reference to reality, 
that assumption is justified. To make this uncon- 
sciously implied meaning clear to the mind is to 
make an advance in knowledge and in clearness of 
thought. With the individual, as with the race, 
knowledge of meaning is at first very imperfect, and 
consists in a few of the striking qualities common to 
the objects to which the name is applied. The 
essential thing for the purposes of ordinary communi- 
cation is correct reference to reality. If a young 
child is asked what he means by a 'cat,' he will pro- 
bably point to one, if one is in sight, and say ' a 
thing like that.' It is only by judicious questioning 
that he can be led to make explicit in his mind the 
meaning which is really there, and to refer to the 
cat's fur, shape, mode of utterance, power of scratch- 
ing, and other obvious qualities as forming the mean- 
ing or content which ' cat ' has for him. And in 
many cases the application of the name to particular 
examples — its denotation, as it is technically called — 
remains a very prominent part of the meaning to us. 
So long as we have sufficient knowledge of the nature 
of things to guide us in our practical needs, both of 
^ Carveth Read, Logic, Deductive and Inductive, p. 272 

Q 2 



228 THE LOGICAL BASES OP EDUCATION chap. 

thought and of communication, we do not push our 
enquiries further. " To the very last, in most of us, 
the conceptions of objects and their properties are 
limited to the notion of what we can do with them. 
A ' stick ' means something we can lean upon or 
strike with; 'fire,' something to cook, or warm 
ourselves, or burn things up withal ; ' string,' some- 
thing with which to tie things together. For most 
people these objects have no other meaning." ^ It is 
only when, for any reason, we require our knowledge 
of some class of things to be very exact, that we 
strive to obtain a precise definition. The power 
to give an exact definition, then, may be said to be 
a mark of scientific thought, as distinguished from 
the looser thought of every-day life. 

It is now clear that inability to give a precise 
definition is by no means a sign of inability to think 
and speak correctly and intelligently of the matter 
in hand, so far as we require to do so in ordinary 
life. Many people are surprised to find they cannot 
give an accurate definition of such common terms as 
'table' or 'cow,' if they are called upon to do so. 
It does not follow that they know nothing about 
tables and cows. They may even be carpenters 
or graziers, and so know a great deal about them, and 
yet be unable to define their name, though they could 
give a more or less full and accurate description of 
the things to which that name applies. This often 
only means that they have never closely analysed 
their knowledge. In other cases it implies that 
though they know many of the common qualities 
they do not know all those which are conventionally 
regarded as the definition of the name. In all cases 
it shows that the meaning has never been separated 
in thought from the actual things, or the mental 
1 James, Talks to Teachers on Psychology, p. 59. 






XVI DEFINITION AND CLASSIFICATION 229 

images of those things, in which that meaning is 
exemplified. 

It follows that the definition of an unfamiliar 
word, no matter how correct it may be, may convey 
little or no information to one who, by analysis of 
other cases, has never reached the elements which 
are combined in that definition. As Dr. Venn 
says : "It must be understood . . . that definition 
is but one way, and this a somewhat technical 
way, of conveying a meaning to any one who is 
in doubt. To raise the requisite experience at first 
hand, or by exercise of imagination, may often be 
the most effective plan." ^ In brief, definition is 
always abstract, and says but little to those who, 
like young children, cannot detach their thoughts 
from the concrete experiences of life. Definition, 
like the recognition of law, is the end, not the begin- 
ning, of a process of acquiring knowledge. 

§ 5. — Again, the unit of thought-expression is the Limits of 
sentence ; the idea contained in the sentence is ^ "^ ^°^^* 
grasped as a whole, and not built up by joining 
together the meanings of the individual words 
which constitute it. It follows that the power to 
understand a sentence in its context, and the power 
to define the separate words of which that sentence 
is composed, are largely independent of each other ; 
either may exist in the absence of the other. 
We see, then, that in actual thought the demand for 
a definition is always more or less exceptional. And 
when such a demand is made, it always implies both 
knowledge and ignorance. There is ignorance of the 
true force of this particular word, but knowledge of 
much of the context in which it occurs. Without 
this combined knowledge and ignorance the mind 
would not ask for a definition. Such a demand may 
1 Op. ciL, p. 279. 



230 THE LOGICAL BASES OF EDUCATION chap. 

be satisfied either by an appeal to authority or by a 
personal investigation of the facts. The former is, 
of course, the more rapid and usual method, but the 
latter, if thoroughly carried out, leads to the more 
thorough knowledge. It is well, then, to encourage 
the search for definition. But it must be recognized 
that there are limits to such a search, for every 
word cannot be defined. We can get to nothing 
more simple than the final results of an analysis of 
sense-impressions. We can analyse an actual object, 
for instance, into its weight, form, colour, &c., and 
we can analyse the form into its geometrical elements. 
But we cannot go further than this, and when we 
have reached the end of the analysis we have reached 
the limit of the power of definition. We cannot 
define 'blue,' or 'sweet,' or 'pleasant'; for we have 
no simpler forms of language to express such un- 
analysable elements of experience. 
Meaning of Again, all definition implies common qualities 
Names. possessed by a class, but separated in thought from 
the individuals in which they are found. In the 
class of words known as ' Proper Names ' this separa- 
tion never takes place. The very term 'proper' 
implies that such a name is peculiar to the individual 
who bears it. A proper name is not given to a 
person or place because of the presence of certain 
qualities ; therefore, it does not imply any qualities 
common to the various individuals who may happen 
to bear the same name. All ' men' are related to 
the general idea 'man,' as instances in which 
that general idea is exemplified. But there is no 
such general idea corresponding to ' Smith ' or 
' Jones.' Each particular Jones has, of course, 
innumerable attributes, and these are known more or 
less to his friends, and give meaning to his name. 
But the name is not given because he possesses those 



XVI DEFINITION AND CLASSIFICATION 231 

attributes, and it would continue to be given if they 
were fundamentally changed. " Macaulay after his 
mind was gone was still Lord Macaulay and his 
father's son, but what else was he that he had been 1 "^ 
And the attributes of one individual bearing a certain 
proper name differ from those of every other indi- 
vidual who bears it. " The same word ' John ' means 
one person to me if I use or hear it in one company, 
and quite another in a different society." ^ No doubt, 
each John has attributes in common with other 
Johns, but the proper name does not imply any of 
those attributes. The name does not rest on any 
analysis of qualities, as does every general name, but 
is given to the individual as one definite piece of 
reality. Hence " the name of an individual means 
all that that individual is, but precisely on that 
account it is not such as a general name." ^ A 
proper name has, then, no general meaning which can 
be expressed in a definition ; its meaning is always ' 
individual, and serves only as a means of identifi- 
cation. 

§ 6. — Having reached a definition, we must next Rules of 
ask whether it is satisfactory. There are certain 
recognized rules to which a logically perfect definition 
must conform, but these are to be regarded not so 
much as directions for forming a definition as tests 
of their merit after they are formed. 

(1) With regard to content, the one and sufiicient 
condition of validity is that the definition precisely 
states the recognized connotation of the word, and 
nothing else. If it includes a ' property ' the 
definition is made unnecessarily long and cumbrous ; 
if it mentions an ' accident ' it may unduly limit 

1 Bosanquet, Logic, vol. i., p, 54. 

'^ Hobhouse, The Theory of Knowledge, p. 106. 

3 Ibid., p. 107. 



232 THE LOGICAL BASES OF EDUCATION chap. 

the application of the definition ; if it omits part of 
the connotation, its application may be improperly 
extended. 

(2) With regard to expression, the aim is to 
secure definiteness and precision. Thus the definition 

{a) Should not he mere tautology. 

(b) Should not be stated in vague language. 

(c) Should not he negative unless the whole 
TYieaming is a negative one. 

With regard to {a), the content of an idea is 
evidently not expressed by giving that idea a new- 
name. For example, to say " Veracity is truth," 
does not state the qualities of character and conduct 
which compose our idea of the virtue in question. 
It by no means follows, however, that such tautologies 
are useless. They generally consist in affirming that 
a new and unfamiliar term means exactly the same 
as a familiar one. A child might well know what 
truth is, and yet not recognize it under its new- 
label of " veracity " ; to learn that the two terms 
are synonymous increases his knowledge of language 
though not of virtue. The common definition, 
" A noun is a name " comes under this head. 
Logically it is a tautology, but practically it enables 
the child to ticket a familiar idea with a technical 
label. To ask him to define a name would simply 
be to confuse him, for it would be to insist on 
an analysis of an idea so simple to him that no 
analysis is required, and no analysis would make it 
clearer. 

(h) The demand for clearness is mosfc important. 
The definition of a name as " a word taken at pleas- 
ure to serve for a mark which may raise in our minds 
a thought like to some thought we had before, and 
which, being disposed in speech and pronounced to 
others, may be to them a sign of what thought the 



XVI DEFINITION AND CLASSIFICATION 233 

sp'eaker had or had not before in his mind," ^ what- 
ever may be its merits for a philosophical enquiry into 
language, obviously does not make the idea clearer 
to the ordinary mind. Similarly, a child would proba- 
bly not receive much assistance in understanding 
what " network " is from the definition given by Dr. 
Johnson — "anything reticulated or decussated at 
equal intervals, with interstices at the intersections." 
Such examples make it clear that a pedantic insist- 
ence on definition may do much to hinder the com- 
prehension of meaning. The ordinary dictionary 
recognizes this, and the majority of the ' definitions ' of 
the words of common language which it contains are 
descriptions rather than definitions in the logical 
sense. Common sense tells us that such descriptions 
are often exactly what we want. To see a net and 
think out its purpose gives more content to the idea 
than to learn not only such a definition as that of 
Dr. Johnson, but any definition that could, in all 
probability, be framed. 

(c) The rule against negative expression is really 
included in that for content, for to say what a 
thing is not is certainly not to give its conno- 
tation, the function of which is to say what it 
is. Euclid's definition of a point is an example 
of this fault. It omits the essential positive quality 
of position in space, and it is only because we 
are led to interpret it spatially by the influence of 
the context in which it occurs, that we can give 
any meaning to it at all. A few words whose 
meaning is essentially negative — such as unequal, 
alien — are, however, most aptly defined in a negative 
form. But it should be borne in mind that the mere 
presence of a negative prefix does not limit a word 
to a purely negative meaning; 'unhappy,' for ex- 
^ Hobbes, Computation or Logic, cli. ii. 



234 THE LOGICAL BASES OF EDUCATION chap. 

ample, means more than mere absence of happiness, 
it implies the presence of a certain amount of positive 
misery. 

§ 7. — So far we have considered only definition, but 
it must be remembered that definition and classifica- 
tion are correlative, and proceed together. Turning 
now to this other aspect, we see first that classification 
is a mental organization of experience on the grounds 
of recognized resemblances and differences. This 
includes, in the first place, the grouping of particular 
things, as of a number of objects under the term 
*rose,' and, secondly, the grouping of classes, as 
' rose ' and ' lily ' under ' flower.' That all classifica- 
tion is a mental construction must be insisted on. 
In exceptional cases such an organization may be 
carried out in the material world, as in a museum or 
library ; but even then it existed mentally first. In 
other words, every class implies a definition, for it is 
based on the explicit recognition of a common nature. 

Now it is evident that any particular thing can be 
thought under many classes. • Every quality we can 
detect in it is a possible basis for classification. 
We could, for example, class all the material objects 
in the universe under distinctions of colour, and to 
some extent the artist does so. In practice we are 
guided by common sense and common speech, which 
embodies in this respect the common sense of our 
ancestors. We try to classify things so that the 
classification will be most serviceable to the special 
purpose we have in hand. The botanist and the 
medical man, for instance, would classify plants in 
very different ways, the market-gardener would give 
yet another classification, and so on. And to these 
various classifications would correspond various spe- 
cial definitions. This explains why a word often has 
a meaning in some particular science different, to 



DEFINITION AND CLASSIFICATION 



235 



some extent, from its meaning in ordinary speech. 
The definitions of ordinary language are based upon 
the classification which deals in the most general 
way with the whole nature of the objects classified ; 
whilst those of a particular science may be based on 
a classification which emphasizes only one side of 
that nature. 

§ 8. — The first and most obvious aim of every 
classification is to group exhaustively the whole 
denotation of the class-name, in such a way that the 
groups are exclusive of each other. This can only 
be secured if we confine ourselves to one basis in 
each step of the classification. To put the matter 
symbolically : If we have a class G which exhibits a 
quality D throughout its members, but in various 
forms dj dg . . . dn, we may make D the 
principle on which we divide the wider class or 
Genus G, into the sub-classes, or Species, S^ Sg . . . 
Sw — 

G (D) 



Rules of 
Classifica- 
tion. 



(-Gdi) (-Gda) 



:GdJ. 



Here the classification is correct provided that in 
denotation 

81 + 82+ .... S^ = G. 

This implies — 

(1) That no individual is found in more than one 
class. 

(2) That every individual which comes under G 
is found in one of the groups S^ Sg . . . ^n- 

S 9.— If we examine the connexion of this ciassifica- 
with definition we see that D is not part or the Definition, 
definition of G, because it appears under various 
forms. But it is part of the content or total 



236 THE LOGICAL BASES OF EDUCATION chap. 

meaning of G, or we could not use it as a basis for 
division. We have, therefore, enclosed it in brackets. 
If now we turn to the definition of the sub-classes, 
we see that every one of them possesses all the 
attributes included in the definition of G, and that 
they are marked off from each other by the various 
modifications of D, viz., d^ dg . . . d^. These are 
technically called the Differences of the co-ordinate 
species. Hence, it is evident that we may suffi- 
ciently define S^ when we state its genus (G), and 
the particular difference (d^), which marks it off 
from co-ordinate species under the same genus. In 
other words : in definition or connotation 

Sj = Gdj ; S2 = Gd2 ; . . . . S^ = Gd,,i. 

This is not only the most convenient, but also the 
most scientific way of expressing a definition, as it 
assigns both the place of the species in the classifi- 
cation and the basis on which that classification is 
made. It recognizes, too, that a demand for defini- 
tion implies considerable, though incomplete, know- 
ledge of the matter in hand ; it assumes that both 
G and D are known. 

As a concrete example we may take — 

Plane Triangles 



i I I 

Equilateral Isosceles Scalene 

Triangles Triangles Triangles 

Here the basis (D) is the mutual relations of the 
lengths of the sides, and of this we find three, and 
three only, possible modifications : equality of all three 
sides ; equality of two only ; inequality of all. 
Hence the classification is correct. The same genus 
might be classified on the basis (Da) of the relations 
of the angles into right-angled, obtuse-angled, and 
acute-angled. We have, then, two possible classifica- 



XVI DEFINITION AND CLASSIFICATION 237 

tions, each equally perfect, and each important for 
certain purposes. But they are independent, and to 
mix their results is to vitiate both. No doubt after 
classifying on one basis, we may proceed to apply 
the second principle to as many of our species as it is 
adapted to, and so take a second step in classification. 
For example, the three-fold classification on the basis 
of the relation of angles can be applied to the species 
isosceles and scalene in the classification based on the 
relations of sides, but not to the species equilateral. 
, Much confusion is frequently caused by neglect of 
this necessity for singleness of basis. Many school- 
books on grammar, for example, classify nouns into 
Proper, Common, and Abstract, where two bases are 
confused together, for the distinction between Proper 
and Common is founded upon the scope of the appli- 
cation of the name, whilst Abstract — which should 
be correlative with Concrete^ — refers to the kind of 
existence of the things named. 

Or again, sentences are often divided into Simple, ciassifica- 
Principal, and Subordinate, which brings in yet pa^tmon. 
another confusion. For whilst Simple and Complex 
are species under the genus Sentence, Principal and 
Subordinate Clauses are constituent parts of a com- 
plex sentence, and not species under that genus at 
all. As we have seen, we can define a species by 
naming its genus and difference, but we cannot say 
that a subordinate clause is a certain kind of com- 
plex sentence. The division of a complex sentence 
into its clauses is, then, an act of partition similar to 
dissecting a flower or an animal ; its results are 
constituent parts of a whole, not species under a 
genus. This distinction must be clearly borne in 
mind ; to enumerate parts which together constitute 
a whole, as, e.g. the counties of England as making 
up England, is quite a different mental process from 



238 



THE LOGICAL BASES OF EDUCATION chap. 



enumerating species under a genus. One test of a 
logical classification always is that the genus can be 
predicated of each of the species. 

§ 10. — We have seen that not only individuals, 
but classes can be grouped. In the examples we 
considered, each step of classification was on a new 
basis. Such a classification may be called Disjunctive ; 
its whole aim is to give an exhaustive enumeration 
of particulars on the basis of certain resemblances. 
The value of such an arrangement is, as we have seen, 
relative to the special purpose with which it is made. 
So long as men thought the world was of com- 
paratively recent origin, and that the different species 
of organized beings were unchangeable and divided 
from each other by gaps which never had been 
crossed, and never could be crossed, such a classifi- 
cation was all that was aimed at. It is emphatically 
the kind of organization of knowledge sought on the 
plane of sense-perception. Nor did the investigations 
of modern science at once change the aim. It was 
only when such researches as those of geology 
showed the immense age of the world, and demon- 
strated that existing species are really modern 
successors to species very different in character, that 
a new aim in classification was consciously adopted 
in science. This aim was to take a single principle 
as operative throughout the whole classification. 

§ 11 . — The classification thus became Suhsumptive, 
that is, each sub-class was given a definite place in a 
hierarchy of classes exhibiting successive develop- 
ments of one principle. In special cases, such 
classifications had, no doubt, been made at all times, 
e.g. the ordinary alphabetical arrangement of an 
index or a dictionary is based throughout on the 
conventional order of letters in the alphabet. And 
there is reason to think that in other cases such 



XVI DEFINITION AND CLASSIFICATION 239 

a principle was really operative before it was con- 
sciously recognized. For it is obvious that we may 
classify by starting with a distinctly apprehended 
principle and proceed to develop its differences, or 
we may start with particulars and try to group them 
so as to bring out some principle. In this latter 
case the principle is operative before it is appre- 
hended. As Darwin said, " Community of descent 
is the hidden bond which naturalists have been 
unconsciously seeking, and not some unknown plan 
of creation, or the enunciation of general propositions, 
and the mere putting together and separating objects 
more or less alike." ^ 

When one governing principle such as this is 
operative throughout, each class has a definite and 
fixed place in the classification. Thus the two 
terms, genus and species, require to be supplemented, 
and in the biological sciences we have such terms 
as * order ' and ' kingdom ' wider than genus, and 
' variety ' as a narrower term. 

The adoption of the genealogical principle also 
affected definition, for it gave quite a new aspect to 
the ' importance ' of attributes. The characters 
which are important for indicating descent are often 
trifling from the point of view of the present life of 
the organism. " It might have been thought (and 
was in ancient times thought) that those parts of the 
structure which determined the habits of life, and 
the general place of each being in the economy of 
nature, would be of very high importance in classifi- 
cation. Nothing can be more false. No one regards 
the external similarity of a mouse to a shrew, of a 
dugong to a whale, of a whale to a fish, as of any 
importance."^ On the other hand, rudimentary 



^ Origin of Species, p. 369. 
^ Darwin, op. cit., p. 365. 



240 THE LOGICAL BASES OF EDUCATION chap. 

organs which now play little or no part in the 
individual's life, are of high importance for indicating 
descent. " Organs in a rudimentary condition 
plainly show that an early progenitor had the organ 
in a fully developed condition ; and this, in some 
cases, implies an enormous amount of modification 
in the descendants." ^ The general or natural 
classification of organic beings is then " founded on 
descent with modification." ^ The dominant principle 
throughout is productive power. 

Nor is this principle by any means confined to 
biology. "If we possessed a perfect pedigree of 
mankind, a genealogical arrangement of the races of 
man would afford the best classification of the various 
languages now spoken throughout the world ; and if 
all extinct languages, and all intermediate and slowly 
changing dialects, were to be included, such an 
arrangement would be the only possible one. Yet 
it might be that some ancient languages had altered 
very little and had given rise to few new languages, 
whilst others had altered much owing to the spread- 
ing, isolation, and state of civilization of the several 
co-descended races, and had thus given rise to many 
new dialects and languages. The various degrees of 
difference between the languages of the same stock, 
would have to be expressed by groups subordinate to 
groups ; but the proper or even the only possible 
arrangement would still be genealogical ; and this 
would be strictly natural, as it would connect 
together all languages, extinct and recent, by the 
closest affinities, and would give the filiation and 
origin of each tongue."^ 

We see the same principle of causation or produc- 
tive power as the basis of classification applied 

1 Darwin, op. cit., p. 424. ^ jfyid,^ p. 369. 

3 Ibid., p. 371. 



XVI DEFINITION AND CLASSIFICATION 241 

more and more widely. " There is the physical 
classification into Solids, Liquids, and Gases. But 
these states of matter are dependent on temperature ; 
at least, it is known that many bodies may, at 
different temperatures, exist in all three states. 
They cannot therefore be defined as solid, liquid, or 
gaseous absolutely, but only within certain degrees 
of temperature, and therefore as dependent upon 
causation. Similarly, the geological classification of 
bodies, according to relative antiquity (primary, 
secondary, tertiary, with their subdivisions), and 
mode of formation (igneous and aqueous), rests upon 
causation ; and so does the chemical classification of 
compound bodies according to the elements that 
enter into them in definite proportions."^ It is 
because the same principle cannot be applied to the 
elements themselves that chemistry remains so largely 
empirical. 

We see, then, that throughout the realm of know- 
ledge the idea of process is displacing the idea of things 
as the essential factor in reality. This is the natural 
result of the development of thought from the stage 
of sense-perception, through that of law, to that of 
system. To concentrate the attention of the young 
mainly on ' things ' is, then, to arrest their mental 
development. 

§ 12. — Of course the work of classification is not 
complete, and indeed, one does not see how it ever 
can be, for in the long ages of the past many data 
necessary to give such completeness to our present 
knowledge have utterly perished. But as knowledge 
advances, so the arrangement of contents of reality 
becomes more systematic and more accurate. Still, 
classification, like its correlate definition, can never be 

1 Carveth Read, Logic, Deductive and Inductive, pp. 267 — 



242 THE LOGICAL BASES OF EDUCATION chap. 

regarded as permanent, for such changes as have taken 
place in the past are going on in the present and may 
be anticipated in the future. As past types have been 
replaced by those we know, so they in turn will give 
place to others. Evolution is a matter not of the 
past alone, but of the present and future as well. 
However, the changes are very slow, and an existing 
classification may well hold for many thousands of 
years. Whilst then, as Mr. Carveth Read well puts 
it, " a classification . . . represents a cross-section of 
nature as developing in time," ^ yet that cross-section 
largely corresponds to our knowledge. Our aim is 
to account for it. We may symbolize the develop- 
ment in time by a tree with its roots, trunk, branches, 
twigs, &c. We are amongst the branches and twigs, 
and we try to trace back their connexion with the 
root and so to get a knowledge of the kind of 
process which is developing. It may be that we 
must be forced to rest satisfied with tracing our 
origins back only to a few main branches ; but even 
then we have gained much insight into that general 
principle of development which is the life of the 
universe. 

§ 13. — When a principle of development is made 
the basis of a classification there is but one step to 
explanation. But it is an important step. For 
classification merely describes and arranges ; it gives 
no reason why the resemblances and differences on 
which it is based are what they are. It is the 
function of explanation to assign these reasons. This 
step is taken when the principle on which the classi- 
fication is based is shown to be a law of change 
actually operative in reality. In biology when it 
was shown that variations are in fact transmitted by 
heredity, and that the variations which survive are 
1 Op. cit., p. 266. 



XVI CLASSIFICATION AND EXPLANATION 243 

those which aid the possessors in the struggle to 
maintain existence, it was possible " to comprehend 
and follow out in some detail those changes in the 
form, structure, and relations of animals and plants 
which are effected in short periods of time, geologi- 
cally speaking, and which are now going on around 
us." ^ Such changes are shown to be necessary con- 
sequences of the operations of natural law. So 
always ; explanation consists in bringing under law. 
A fact is to some extent explained when it is shown 
to be an instance of a law of causation ; an empirical 
law is explained when it is shown to be resolvable 
into wider and more elementary laws. 

Professor Lloyd Morgan gives an instructive illus- 
tration of this, which we will venture to borrow : 
" A good many years ago, when I was a young 
student, a clever lad in Cornwall asked me the old 
question, ' Why does a stone fall to the ground ? ' 
Not wishing to put him off with the long-sounding 
words, ' Universal gravitation,' I replied, " Because it 
is heavy. ' ' But a feather is not heavy and yet it 
falls to the ground,' was the prompt answer. I replied 
that the feather was relatively heavier than the air. 
The lad was silent for a moment, and then said, 
' That's just one of the things I want to know : 
does the air fall to the ground and collect there like 
water in a pond, only we cannot see it because we 
are in it and it is invisible 1 ' I saw that this lad's 
powers of comprehension were fully equal to the 
occasion, and explained the whole matter as best I 
could. I told him that he was quite right in sup- 
posing that the air, like the stone and the feather, 
was attracted by the earth ; I pointed out the 
universality of gravitation as a law of nature ; 
and then reverting to his first question, I said, 
^ Wallace, Darwinism, p. 7. 

R 2 



244 THE LOGICAL BASES OF EDUCATION chap. 

* You now see that we explain the fall of the 
stone as a particular case of the action of a law that 
is universal in its generality.' He was again silent 
for a moment, and then asked, ' But what makes the 
earth attract it after all? ' I laughed, and said, 
' You're a philosopher ! Nobody can answer that 
question. Perhaps you may live to find it out, or at 
any rate to understand the solution when it comes, 
as come it may.' " ^ 

§ 14 — It must be acknowledged, then, that there 
are limits to all explanation. We cannot explain the 
ultimate nature of reality. The demand of thought 
is satisfied when concrete experiences can be shown 
as the interconnexions of general laws. " The com- 
posite is explained by construction out of the 
elementary ; the elementary by interconnexion in a 
system ; the system as a totality is that which 
requires no explanation, being itself the explanation 
of all its component parts." ^ 

It is further evident that in some cases we can 
push explanation further back than in others. The 
extent to which this can be done in any science 
indicates the advancement of that science towards 
perfection. When a science is complete " we are 
able by long chains of deduction to infer the indi- 
vidual fact without need of verification." ^ Thus 
physics and astronomy are much nearer perfection 
than is chemistry or medicine. 

§ 15 — All logical explanation, then, brings the 
particular under universal laws on the ground of 
fundamental identity. If the identity is not essen- 
tial the explanation is a vain one. " Hence the 
attempts to help the understanding by familiar 



1 Psychology for Teachers, pp. 128 — 129. 

^ Hobhouse, The Theory of Knowledge, p. 449. 

3 Ibid., p. 404. 



XVI CLASSIFICATION AND EXPLANATION 245 

comparisons are often worse than useless. ... The 
proneness to substitute familiarization for radical 
explanation is the easily besetting sin of human 
understanding : the most plausible of fallacies, the 
most attractive, the most difficult to avoid even 
when we are on our guard against it." ^ Such 
explanations are only illustrations by analogy, and 
their value depends on the strength of the analogy.^ 
But it must be noted that 'explanations' of this 
kmd are frequently the only ones which can be given 
to individual enquirers, for nothing is explanation to 
the individual which does not bring the new fact 
under what is already known to him. Care must then 
be taken that such an explanation is valid as far as 
it goes, that is, that the analogy is a strict one, or 
rather that both the thing explained and the relation 
which illustrates it are cases of the same wider law 
Thus the late Professor Clifford wrote: "It is an 
explanation of the moon's motion to say that she is 
a falling body, only she is going so fast and is so far off 
that she falls quite round to the other side of the earth, 
instead of hitting it, and so goes on for ever.''^ But 
when he goes on to add : "But it is no explanation 
to say that a body falls because of gravitation," on 
the ground that " this attraction of two particles 
must always, I think, be less familiar than the 
original falling body," ^ he is limiting 'explanation' 
to mere familiarization, and excluding from the term 
what IS Its very essence. In other words, he is con- 
fining explanation to a psychical phenomenon, a mere 
efiect on an individual mind, and excluding it from 
Its true place as the crowning point of logical 
theory. 

^ Cf7v^lfl~S ^''^'''' ^'^'^^^^"^^ «*^^ Inductive, p. 238. 
3 Lectures and Essays, pp. 102—103. 4 /^^-^ 



CHAPTER XVII 



LOGIC AND EDUCATION 



General 
Relation of 
Logic to 
Education. 



§ 1. — We are now in a position to see the general 
bearing of logic on education. The function of 
education is to lead the child to find his true place 
and his true work in the universe. But before he 
can feel at home in the world, he must, at least to 
some extent, understand it ; so long and so far as he 
does not understand it, he is, as it were, a stranger 
in it. Logic analyses the process by which this 
knowledge and understanding of the universe have 
been gradually attained by the human race, and 
thus indirectly gives guidance to the educator in his 
task of leading the individual along the same path. 
The educator has to guide each pupil from the 
beginnings of knowledge in sense-perception, through 
the second stage of recognition of law, into the 
third stage, in which it is seen that all laws must 
find their reason and explanation in system. 

It seems obvious that he who has made this 
process clear to his own mind will be better fitted to 
guide others than he who has not done so. He 
should have acquired logical habits of thinking, and 
these habits will influence his conduct and his 
teaching. Logic will not make him reason well, but 



CH. XVII LOGIC AND EDUCATION 247 

it will help him to do so. And it will do this not 
only positively but negatively. For the study of 
the characteristics of correct thought involves the 
apprehension of the various forms of error to 
which thought is liable. Against these one is more 
likely to be on one's guard when one knows their 
nature than when one does not. Moreover, a study 
of logic makes it easier not only to suspect the 
existence of error but to recognize its exact char- 
acter. Logic will, then, help the teacher both to avoid 
inaccurate thought himself and to correct any such 
inaccuracy in his pupils by making evident to them 
the source of the error. And this is very necessary, 
for owing to the limitations of their experience and 
knowledge, children are prone to make very rash 
inferences. 

Nor have we in all this a reference only to the 
intellectual side of education. The uni-verse which 
a child must learn to understand is a social and a 
moral universe as well as a physical one ; the facts 
of experience with which he starts are found in his 
relations to his fellows as well as in those of the 
material world. In these facts, too, he must find 
laws, and through laws he must pass to the con- 
ception of that moral system, in which alone he can 
find the true freedom of rational and self-realizing 
activity. Clearly to conceive a purpose and intelli- 
gently to adapt means to its attainment, to weigh 
the evidence for and against a line of conduct, are 
mental activities which have a direct reference to 
the moral life. Indeed, to separate intellectual 
from moral training is to hinder and not advance that 
true development of the pupil which it is the function 
of the educator to promote. For, as Mrs. Bryant 
says : " True development is the development of that 
mind, which is set, throughout, on the attainment, 



248 THE LOGICAL BASES OF EDUCATION chap. 

in its world, of those objects which it takes to be 
right, and on the understanding of that world so 
that it may be sure of their rightness. In such 
development it realizes freedom and wisdom for itself, 
and furthers the like realization by others." ^ 

Logic, then, has a bearing on the whole educa- 
tional process, so far as that process is rational. 
But the educator must not expect detailed guidance 
in his work from logic any more than from psycho- 
logy. Both sciences give general guidance only. 
Psychology investigates the forms of actual mental 
activity common amongst men and children, and, 
therefore, a study of psychology aids the educator 
by suggesting to him the best ways of awakening 
such activity. Logic, on the other hand, is regula- 
tive, and helps the educator to determine the general 
lines on which such activity should proceed to attain 
the goal of knowledge. By the character of his 
teaching the teacher largely determines the character 
of the thought-processes in his pupils. If the former 
is unmethodical and ill-arranged, if it permits invalid 
inferences, or encourages rash and unwarranted con- 
clusions, then the pupils will not be helped to think 
clearly and accurately, but will rather be hindered 
from doing so. But if, on the other hand, the 
teacher's presentation of every subject is well- 
arranged, if his inferences are not only just but 
shown to be just, if the importance of weighing 
evidence is insisted on, and no conclusions accepted 
which the evidence at hand does not warrant, then 
the pupils are being unconsciously trained to habits 
of accurate thought. Thus all teaching should be 
* logical ' in the sense that it should be the expression 
of methodical and valid thought. 

But the subject-matter of the thought, and the 
^ Educational Ends, p. 290, 



XVII LOGIC AND EDUCATION 249 

consequent character of the knowledge gained by the 
pupils can be determined neither by psychology nor 
by logic. As we saw in an earlier chapter, logic 
examines into the general nature of the processes by 
which knowledge is attained. Whether the general 
conditions of knowledge thus brought to light are 
fulfilled in any particular case must be left to the 
special science in question to determine. Similarly, 
the particular details of logical arrangement in any 
piece of teaching cannot be decided by an appeal to 
logic alone. Logic warns us to insist on sufficient 
evidence ; but logic alone cannot decide when the 
evidence is sufficient. From it we gather the 
general conditions of sufficiency, but other know- 
lege must determine how far those conditions are 
fulfilled. Hence, logic, like psychology, gives only 
the broad, general, and abstract bases of educational 
method. But the guidance thus supplied may at least 
help us to avoid the somewhat sweeping criticism 
of Ruskin that " Modern ' education ' for the most 
part signifies giving people the faculty of thinking 
wrong on every conceivable subject of importance to 
them."i 

§ 2. — The first pointwhich logic emphasizesin educa- Education 
tional theory is that all true education must be relative socfety. 
to the society in which it is given. It is an error far 
too common to consider education exclusively from the 
point of view of the individual child. But a child 
is not merely an individual. He is equally a member 
of a social organism, and into the life of that organ- 
ism he is born as surely as he is born to his own 
individual life. Indeed, he is an individual only 
because he is a member of the social organism, and, 
therefore, his true individuality is expressed, and his 
true nature realized, so far, and so far only, as he 
^ Sesame and Lilies, p. 38. 



250 THE LOGICAL BASES OF EDUCATION chap. 

shares the common organic hfe. Education has to 
prepare him to live his life in a society which has 
attained a certain stage of civilization and know- 
ledge. It cannot do this by ignoring these factors. 
Hence it is evident that we may be led very far 
wrong if we adopt as more than the broadest of 
general principles the maxim that "the educa- 
tion of the child must accord both in mode and 
arrangement with the education of mankind, con- 
sidered historically." ^ This inference from the 
general parallelism between the development of the 
individual and that of the race has been a favourite 
principle with many educators since the time of 
Pestalozzi. And it is true that "in the education 
of the mind of the race, as in that of the individual, 
each different age and purpose requires different 
objects and different means ; though all dictated by 
the same principle, tending towards the same end, 
and forming consecutive parts of the same method." ^ 
But to carry the principle so far as to find the only 
suitable material for the nourishment of the youthful 
mind in the intellectual products of the childhood of 
the race is to ignore many most important facts. 
As the modern child is a member of a very different 
social organism from that in which his savage ances- 
tors lived, so his mental life is different from theirs. 
He finds all around him a different way of interpreting 
the facts of experience, different views of what is 
right and what is wrong, different conceptions of life 
and duty. All these he insensibly absorbs, for he 
learns to think and talk in a language which en- 
shrines them all, and they profoundly modify the 
development of his mind. Though the products of 
primitive times, therefore, appeal to one factor of his 

^ Spencer, Education, p. 67. 

2 Coleridge, The Friend, vol. iii., pp. 180—181, 



XVII LOGIC AND EDUCATION 251 

individuality, they appeal to one only, and, as a con- 
sequence, they are not fitted to supply all the mental 
nourishment which he requires. In many cases. 
indeed, expressing as they do a stage of morality 
which was, in many points of practice, actually an- 
tagonistic to our own, they are quite unsuitable for 
leading a child to a comprehension of the morality 
which we desire him to learn to live. Such a mis- 
reading of the task of education is the result of 
ignoring the bearing of logic on educational theory 
and practice and basing both on an individualistic 
psychology. So we are continually told that educa- 
tion means development. It does, but it means 
something more. Education is not mere develop- 
ment, it is training; and training implies an end 
clearly conceived by the trainer, and means carefully 
organized to attain that end. The child is much too 
immature to understand what he should aim at 
being, or consistently to pursue his purpose if he could 
conceive it. The educator's task is to assist in pro- 
ducing that which the child would wish to develope 
for himself had he a clear idea of his own nature, but 
which he will never reach if left to himself. It is 
this external and universal aspect of education which 
the reference to logic emphasizes. 

This aspect is seen on the intellectual as much 
as on the moral side of the educational process. 
Here we must take as our axiom that knowledge 
exists, that laws and theories have been proved and 
shown to be true. This proof has been a process 
going on throughout the ages. With many a wandering 
by the way men have come in many cases to recognize 
the true connexion between the evidence they have 
and the conclusions which may be drawn from it. The 
child must also be led gradually to appreciate the force 
of this same evidence. But his process is a more 



252 THE LOGICAL BASES OF EDUCATION chap. 

direct one, for it is along a path determined for him 
by his teacher. He escapes the wanderings, but he 
follows the same general route. In this sense his 
development is parallel with that of the race, and 
the teaching is on historical lines. But there is 
another element. In the determination of the objects 
studied, in the arrangement of the stages of study, 
in the use of scientific apparatus of various kinds, we 
have that element of appeal to authority which can 
never be absent from education. For in all these 
we have the immature child accepting with unques- 
tioning faith the results of much slow mental work 
on the part of others. The child, for example, does 
not question the accuracy of his microscope, but the 
microscope embodies much knowledge of physical 
laws ; these laws, in using the microscope, the child 
accepts on authority. Only so can he enter into the 
heritage of knowledge to which he is born. 

§ 3. — The next great lesson that logic, equally with 
psychology, teaches the educator is that the attain- 
ment of knowledge is the result of mental exertion. 
To educate is to train to think, for by active 
thinking alone is knowledge attained. Without 
active thought we cannot get beyond mere belief, for 
to pass from belief to knov/ledge means to sift and 
weigh evidence for oneself. This was clearly seen by 
Plato, and has been frequently insisted on by later 
philosophers, but it has been yet more frequently 
forgotten. " Alas ! " says Coleridge, " how many 
examples are now present to my memory, of young 
men the most anxiously and expensively be-school- 
mastered, be-tutored, be-lectured, anything but 
educated ; who have received arms and ammunition, 
instead of skill, strength, and courage; varnished 
rather than polished ; perilously over-civilized, and 
most pitiably uncultivated ! And all from inattention 



XVII LOGIC AND EDUCATION . 253 

to the method dictated by nature herself, to the 
simple truth, that as the forms in all organized 
existence, so must all true and living knowledge - 
proceed from within ; that it may be trained, sup- 
ported, fed, excited, but can never be infused or 
impressed."^ The educator can no more think or 
learn for the pupil than he can breathe or eat for 
him, and true teaching is leading another to think 
and to learn. 

It follows as a corollary from this that there can ^®*^°^.^°J 
be no one mechanical method of teaching such as was 
dreamt of by Pestalozzi when he wrote : "I believe 
it is not possible for common popular instruction to 
advance a step, so long as formulas of instruction 
are not found which make the teacher, at least in the 
elementary stages of knowledge, merely the mechanical 
tool of a method, the result of which springs from the 
nature of the formulas and not from the skill of the 
man who uses it."^ 

This neglects the fact that education has always 
an individual aspect, as it deals with the development 
of particular children. There is no child in general, 
but children differ from each other both generically 
and specifically. They differ generically according to ^ 
their nationality. A German child is different in 
many points from an English child, and both from a 
French child. To dream, then, that a system or method 
of education which has been found successful in one 
nation can be profitably transplanted without very 
serious, and indeed radical, modifications, into another, 
is to fall into a very dangerous mistake, and one which, 
if put into practice, is calculated to do most serious 
mischief. Then again, classes of children belonging to 

1 Op. cit., vol, iii., p. 174. 

"^ How Gertrude Teaches her Children, trans, by Holland 
and Turner, p. 41, 



254 THE LOGICAL BASES OF EDUCATION cha^^- 

lihe same nationality differ according to their social sur- 
roundings, and lastly, individuals brought up in very 
similar surroundings differ in natural disposition and 
endowment. Of all these differences true education 
must take account. The general system of schools 
in a nation must be adapted to realize the national 
ideal ; the kind of aim and walk in life of the 
pupils of each school must be recognized by that 
school ; and the personality of each child in his school 
must be considered by every true teacher. Hence, 
it is obvious that the skill of the teacher can never 
be replaced by any formulas of method. 

Still more paradoxical was the saying of Jacotot 
that with a true method " every one can teach ; and, 
moreover, can teach that which he does not know 
himself." ^ Such an idea shows a fundamental miscon- 
ception of the teacher's functions. He must stimulate 
and guide, and in instruction, as in education 
generally, he must clearly see the end towards which 
he would lead the child, and the path which must 
be followed. He must himself be in possession of a 
system of knowledge before he can help his pupils to 
grasp that system. No doubt he must be able to 
place himself at the child's starting-point, but he 
must see the end of the process at the same time as 
the beginning, with a clearness of which the child 
is incapable. Pestalozzi saw only the first half of 
this truth when he wrote of his experiences at 
Stanz : "I could neither write, count, nor read per- 
fectly .... and really my ignorance of all thest 
things was essentially necessary, in order to brin^ 
me to the highest simplicity of methods of teach 
ing." ^ As method means ordered progress towardr 
a definite end, it is obvious that one who know: 

^ Quoted by Quick, Educational Reformers^ p. 417. 

2 Op. cit.,-p. 22. ''" 



LOGIC AND EDUCATION 



255 



ot the end cannot with certainty determine the 
inethod. 

§ 4. — The conception of education as relative to 
the mental life of society gives us, however, that 
broad guidance as to method which is all that edu- 
cational theory can supply. 

In the Middle Ages, when the conception of the 
rocess of knowledge was confined to deductive 
nference from general judgments universally 
accepted as true, the methods of teaching naturally 
followed the same lines. General principles were 
enunciated by authority, and formed the foundation 
of the whole process. It is a mistake to suppose, 
however, that this made the development of the self- 
activity of the pupil an impossibility. It simply 
determined the direction which that activity should 
take. No doubt there was much merely mechanical 
teaching then as now, but no one who is acquainted 
with the subtleties of the scholastic logicians can say 
that they possessed inactive minds. The mediaeval 
theory of teaching was in relation to the current 
conception of the method of knowledge, and the 
practice was a more or less adequate carrying out 
of that theory. 

With the growth of modern science men's concep- 
tion of the method of knowledge has been consider- 
ably modified. The demand for direct evidence has 
^placed the appeal to authority as the basis of know- 
Ige, and as a consequence, the inductive method 
been largely substituted for the deductive. This 

nge has affected educational practice somewhat 
X wly, and the traditional methods of medisevalism 
\' 1 linger amongst us. But they linger only as 

pses, for unless the methods of education are in 

nony with the current conceptions of the method 
« nowledge, they have no life in them, and the 



Educational 
Method 
Relative to 
Cvirrent 
Conception 
of Know- 
ledge. 



Heuristic 
Methods. 



256 THE LOGICAL BASES OF EDUCATION chap. 

school fails to fulfil its true function in the social 
organism. To attain this harmony the pupil must 
be set to seek knowledge for himself by analysing 
his experiences. Hence arise what are known as 
' heuristic ' methods of teaching, that is, " methods 
which involve our placing students as far as possible 
in the attitude of the discoverer- — methods which 
involve their finding out, instead of being merely 
told about things." ^ 

The employment of such methods is not mainly a 
question of subjects. They are doubtless appro- 
priate in the physical and natural sciences, but they 
are equally applicable to mathematics and the 
humanities. A boy who has by his own efforts 
solved a problem in geometry has made a discovery 
quite as surely as one who has worked an experiment 
in physics or chemistry and drawn an inference from it. 
So a pupil who has exerted his intelligence on a piece 
of Latin prose or an English Essay, who has sorted and 
arranged his ideas, who has compared and weighed 
different modes of expressing his thoughts, has been 
engaged in an original investigation both into the 
subject matter of his theme, and into appropriate 
means of expressing it. Nor can it be denied that 
a pupil who has worked out for himself a topic in 
history, comparing and weighing authorities in the^ 
school fibrary, has been engaged on a true voyage of 
discovery. The essence of heuristic methods is that 
the pupil learns to think for himself, not that he 
learns to do certain things with his hands, though 
that, too, may be involved. There is nothing of the 
heuristic method, for example, if a pupil in a 
chemical or physical laboratory works 'experi- 
ments ' which have been dictated to him by his 

^ Armstrong, The Heuristic Method of Teaching in Special 
Reports on Educational Subjects, vol. ii. , p. 390. 



LOGIC AND EDUCATION 



257 



teacher. To him they are not experiments at all, 
for the essence of experiment is the mental planning 
of what is to be done and the clear conception of 
why it is worth doing. If, on the other hand, the 
pupil does this mental part of the work, it is com- 
paratively unimportant who carries out the actual 
physical manipulation. 

The demand for heuristic methods, then, is not a 
demand for a mainly ' scientific ' course of study. 
" Sense-impression of Nature," said Pestalozzi, " is 
the only true foundation of human instruction, 
because it is the only true foundation of human 
knowledge," ^ and quite a school of educators tell us 
the same thing. But unless a quite unjustifiable 
extension be given to the words " sense-impression 
of Nature," the premise is not true. Human ex- 
perience is not limited to sense-impressions of the 
material world, but includes all kinds of social 
experiences as well, and to exclude all consideration 
of these latter from any stage of education is to 
ensure an imperfect development of the humanity of 
the pupil. 

§ 5. — Educational method must, then, be an active 
process on the part of the pupil, and must show the 
general characteristics of definiteness of starting- 
point and of aim, and of orderly arrangement of 
means, which we saw in chapter viii were ih.e 
essential marks of methodical thought. But here we 
see at once that there must be a material difference 
between the procedure of the original discoverer and 
that of the pupil in school. The discoverer comes to his 
task with abundant knowledge which guides him in 
selecting the material he will study, in concentrating 
attention on this or that aspect of the selected facts 
and disregarding the rest, in forming hypotheses, 

1 Op. cit., p. 200. 

S 



Method of 
Science and 
Method of 
Education. 



258 THE LOGICAL BASES OF EDUCATION chap. 

and in inventing modes of testing such hypotheses. 
The school-boy is in a very different plight. But 
we saw that without such preliminary knowledge all 
advance in knowledge is impossible. It follows that 
the teacher must supply it, and the distinction 
between good and bad teaching is in the manner in 
which this is done. The bad teacher tells the pupil 
certain facts and directs him to do this or that to 
illustrate those facts. The good teacher supplies the 
required knowledge by simply selecting and arrang- 
ing the facts so that this great preliminary difficulty 
is overcome, and then setting the pupil to work on those 
facts by himself. " It is needless to say," writes 
Professor Armstrong, " young scholars cannot be 
expected to find out everything themselves ; but the 
facts must always be so presented to them that the 
process by which results are obtained is made 
sufficiently clear, as well as the methods by which any 
conclusions based on the facts are deduced." ^ 

The essence of good teaching is that it forms accurate 
and methodical habits of thought. But, as we have 
seen, methodical thought is emphatically thought of 
relations and of system. " The absence of method, 
which characterizes the uneducated, is occasioned by 
an habitual submission of the understanding to mere 
events and images as such, and independent of any 
power in the mind to classify and appropriate them. 
The general accompaniments of time and place are 
the only relations which persons of this class appear 
to regard in their statements. As this constitutes 
their leading feature, the contrary excellence, as 
distinguishing the well-educated man, must be 
referred to the contrary habit. Method, therefore, 
becomes natural to the mind which has been accus- 
tomed to contemplate not things only^ or for their 
^ Op. dt., p. 401, 



XVII LOGIC AND EDUCATION 259 

own sake alone, but likewise and chiefly the relations 
of things, either their relations to each other, or to 
the observer, or to the state and apprehension of the 
hearers." ^ 

This apprehension of relations, as we have seen, 
is the work of thought upon the elements which 
result from analysis of experience. But we have 
also seen that it is work of the most extreme diffi- 
culty, and one requiring the most careful sifting of 
evidence. The caution which marks the scientific 
discoverer is, however, far from being a prominent 
feature of the mental activity of childhood. Nothing 
is more characteristic of the untrained mind than 
the rashness with which it jumps to conclusions 
upon utterly insufficient evidence. The tendency to 
generalize every observed relation is natural to the 
human mind, and is both guided and prompted by 
the use of language. A class of children after 
seeing two or three examples of the expansion of 
metals by heat, frequently rushes to the conclusion 
that all metals, or even all solids, expand under 
the action of heat. And too often the teacher 
accepts such a generalization as, with a few ex- 
ceptions, a valid inference. To do this may be to 
teach 'science,' but it most certainly is not to 
teach scientifically. It is, indeed, to cultivate that 
habit of rashness in drawing conclusions, and that 
inability to estimate the force of evidence which it 
is the special task of education to replace by the 
very opposite qualities. The evidence in the sup- 
posititious case we have taken will not even justify 
the assertion that those metals which the children 
have just seen expand under heat will do so under 
all conditions of initial temperature. The generali- 
zation suggested is only the first wild guess of the 
^ Coleridge, op. cit., pp. 107—108. 

s 2 



260 THE LOGICAL BASES OF EDUCATION chap. 

untrained mind ; to treat it as a valid inference is 
to introduce utter confusion into all conception of 
scientific method. Mr. Herbert Spencer objects to 
the teaching of languages, because he thinks they 
encourage dogmatism on the part of the teacher. 
It is to be feared that much of the * science 
teaching' in schools encourages dogmatism on the 
part of the pupils, and one may be allowed to think 
that the dogmatism of ignorance is worse than that 
of knowledge. As Mrs. Bryant well says, "the 
mind which is active needs also to be docile." ^ 

Nor is dogmatism on the part of the teacher by any 
means absent from the ordinary lesson in science. 
In very many cases the evidence which can be 
offered to a class of children in support of a law 
in natural or physical science is necessarily in- 
sufficient to establish that law. As a result, the 
law is guessed at by the children, and either their 
guess is accepted as a valid inference from the facts 
observed, or the teacher rightly treats the guess as 
nothing but a guess, and then tells his pupils 
dogmatically that the guess is known to be a true 
one by evidence which they cannot comprehend. 
This latter course is certainly preferable to the 
former, for the very essence of a good method is to 
mark exactly how far the evidence offered will 
justify the mind in going. The question for infer- 
ence is not the scope or accuracy of the conclusion, 
but the sufficiency of the evidence on which that con- 
clusion is based. One of the chief advantages derived 
from the teaching of natural or physical science 
should be the recognition by the pupils of the 
difficulty of arriving at truth, and of the need of 
caution in making inferences from insufficient 
evidence. It must still be to mathematics and 
1 Educational Ends, p. 265. 



xvii LOGIC AND EDUCATION 261 

languages that the teacher must turn when he wishes 
to train his pupils in drawing conclusions which are 
demonstrably certain, for in those subjects only is it 
generally possible for the youthful mind to grasp all 
the evidence necessary to establish a proposition as a 
demonstrated truth. It is, as we have said, in 
helping a teacher to distinguish between good and 
bad inferences, to estimate when the evidence 
grasped by the mind of his pupils justifies a certain 
conclusion, when one only more or less probable, 
and when it merely suggests a possible line of 
enquiry, that a study of logic has the most practical 
bearing on education. 

§ 6. — It is evident then, that the method of Maxims of 
knowledge as carried out by the child differs 
materially from that of the scientific discoverer, not 
only in that it is guided from without by one to 
whom the whole process and the end to be attained 
are familiar beforehand, but also in its want of both 
exactness and depth. These are characteristics 
which can only come with increased knowledge and 
power of insight, just as the power to work alone 
can only be developed gradually out of work under 
guidance which little by little decreases in amount. 
But that the power of working alone may be 
developed, it is essential that the whole process 
should be carried out. Hence the pupil must be 
taken through inductive processes similar to those 
described in the preceding chapters. He must begin 
by analysis of facts and end with system. If he 
stops anywhere on the way we have a case of 
arrested development. The danger of this, it is to 
be feared, is not sufficiently recognized, and there- 
fore, not adequately guarded against. With the 
insistence on the training of sense-observation, 
which is so fashionable at the present day, there is 



262 THE LOGICAL BASES OF EDUCATION chap. 

some danger that the purely instrumental and pre- 
liminary character of such observation may be lost 
sight of, and that the child may remain in the very 
first stage of knowledge. Even when this danger is 
avoided there remains that of arrest in the second 
stage of abstract law. " Proceed from the concrete 
to the abstract," says a favourite maxim of the 
educational text-books. But this is only half the 
process. The mind should not rest in the abstract, 
but having found abstract relations in the concrete 
facts of experience, it should not only understand 
those facts better, but should also have a key to the 
understanding of many other concrete facts. With 
the concrete we should begin, and with the concrete 
we should end. 

But the concrete with which we start is vaguely 
apprehended as a whole which seems simple to us, 
because our minds have not analysed it and found 
that its elements are many and complex. On the 
other hand, the concrete with which we end is one 
definitely and clearly grasped, because the combined 
processes of analysis and synthesis through which the 
mind has passed have shown it to us as a complex 
whole of inter-related elements. It is this develop- 
ment of the concrete idea which seems to be intended 
by those other common maxims, " Proceed from the 
indefinite to the definite," and " Proceed from the 
simple to the complex." 

It will be seen that these last two maxims refer 
primarily to the kinds of ideas we have of things at 
the beginning and at the end of a process of ac- 
quiring knowledge. Much mistaken teaching has 
been based upon an application of the latter of them 
to the arrangement of the material of instruction. 
For in the case of the matter of knowledge, the 
" simple " are the ultimate and abstract elements and 



XVII LOGIC AND EDUCATION 263 

relations which we reach at the end of a process of 
analysis, whilst the " complex " is the whole piece of 
experience with which that analysis starts. Thus 
interpreted, this maxim is in contradiction to the 
correlative one which tells us to begin with the 
concrete and go on to the abstract. 

A similar correlate to the maxim " Proceed from 
the indefinite to the definite " is that which tells us 
to "Proceed from the known to the unknown." As 
the former refers primarily to the organization of the 
contents of the pupil's mind, so the latter deals with 
the arrangement Of the subject-matter by which that 
organization is carried out. Looked at from the side 
of the contents of the mind, the procedure is from 
the unknown to the known ; for that which is in- 
definite is very imperfectly known, whilst what is 
truly known is definite. 

It is seen, then, that these commonly accepted 
maxims must be taken in connexion with each other 
and woven into a system in order that each may 
bear its proper force, and that they are none of them 
really fundamental principles of method. It may be 
noted, too, that the form in which they are commonly 
expressed, " Proceed from . . . to . . . ," is liable to 
misunderstanding. The words suggest a false view 
of knowledge as consisting of disconnected chains of 
ideas bound together by various bonds of association. 
When I "proceed from" Leeds "to" London, I leave 
the former, and pass many intermediate places before 
I reach the latter. But the true development * of 
knowledge does not correspond to any such serial 
arrangement. Its end is, as we have seen, system, 
and the words " proceed from ... to ... " must, 
therefore, be understood as implying merely that there 
should be a mental process on the part of the learner, 
not that he should leave his starting-point in attain- 



264 THE LOGICAL BASES OF EDUCATION chap. 

ing his end. In true system, starting-point and end 
have become organic parts of one whole construction. 
Rightly and fully understood, the maxim " Proceed 
from the empirical to the rational " is more funda- 
mental than any we have considered, for the "em- 
pirical " are the facts of experience of all kinds, and 
the "rational" is that ultimate system in which 
alone explanation is found. In making explicit the 
method by which this advance can be made, logic 
renders its greatest service to educational theory. 
For the possibility of arrested development of which 
we have spoken is the greatest danger to which 
education is liable. " The good observer . . . may 
not have gone far enough to make him more than a 
good observer ; he may have been stopped by the 
difficulties of abstract attention in clear judgment, or 
his thirst for knowledge in its true form of complete 
unij&cation may have failed him later on. This latter 
case is, perhaps, not uncommon." ^ Dr. Harris ex- 
presses the same fear : " It is believed that arrested 
development of the higher mental and moral faculties 
is caused in many cases by the school. The habit of 
teaching with too much thoroughness and too long- 
continued drill the semi-mechanical branches of study, 
such as arithmetic, spelling, the discrimination of 
colours, the observation of surface and solid forms, 
and even the distinctions of formal grammar, often 
leaves the pupil fixed in lower stages of growth and 
unable to exercise the higher functions of thought." ^ 
It*is only when teachers clearly apprehend the exist- 
ence of this danger, and understand how knowledge 
developes from the lowest stage to the highest that 
our schools will do the work the countrj^ has the right 
to require of them, for only then will they make 

1 Bryar.t, Oj). cit., p. 231. 

- The Psychologic Foundations of Education, pp. 6 — 7. 



XVII LOGIC AND EDUCATION 265 

the most and the best of the rising generation. 
And it is only by making the most and the best of 
any individual that v^e can thoroughly fit him to do 
the most and the best for the community whose 
corporate life he shares. For the nobler, wiser, and 
more skilful a man is, the more fully and perfectly 
will he fulfil those functions which the actual circum- 
stances of his life set before him, which the com- 
munity demands as his duties, and which he will 
himself delight to render, just because, being wise and 
good, he has truly conceived his place and function 
in that system of the universe of which he forms an 
integral part. 



EXERCISES IN INFERENCE 

Analyse the following inferences, determine their 
nature, and estimate their validity — 

1. All these boys are both mischievous and clever ; 
therefore cleverness and a love of mischief go 
together. 

2. A prudent man avoids catching cold ; a man 
cannot be a successful merchant unless he is prudent ; 
therefore all successful merchants avoid catching 
cold. 

3. To say that every rule has an exception is to 
talk nonsense, for as the assertion sets up to be a 
rule, it contradicts itself. 

4. " If thou wert never at court, thou never 
sawest good manners ; if thou never sawest good 
manners, then thy manners must be wicked ; 
and wickedness is sin, and sin is damnation. 
Thou art in a parlous state, shepherd," — Shake- 
speare : As you like it, Act iii., sc. ii. 

5. If all prophets spoke the truth some would be 
believed ; therefore as none are believed it is certain 
none speak the truth. 

6. If boys were always found out and punished 
when they did wrong they would cease to offend ; 



EXERCISES 267 

therefore, the fact that boys do not invariably do 
what is right proves that punishment does not always 
follow their oifences. 

7. A is never found without B, and B is never 
found without C ; therefore C is never found with- 
out A. 

8. Brighton is south of London, and Exeter is 
west of Brighton ; therefore London is north-east of 
Exeter. 

9. I don't believe it, for I saw it in a newspaper, 
and newspapers are always telling lies. 

10. Jones must succeed in the world, for he is an 
honest man, and dishonest people never prosper. 

11. If a man has been properly taught he can 
teach, for experience is all that is wanted in 
teaching. 

12. "When a fact is supported by no more than 
the statement of a single man, however honest he 
may be, historians ought not to assert it, but to do 
as men of science do — give the reference (Thucy- 
dides states, Caesar says that . . . ) ; this is all they 
have a right to affirm." — Langlois and Seignobos, 
Introduction to the Study of History, p. 197. 

13. "If our printed books, after the successive 
revisions of author and printer's reader, are still but 
imperfect reproductions, it is only to be expected that 
ancient documents, copied and recopied as they have 
been for centuries with very little care, and exposed 
at every fresh transcription to new risks of altera- 
tion, should have reached us full of inaccuracies." — 
Ihid., p. 73. 

14. "The Rev. Hilderic Friend vouches for the 
genuineness of the following story : . . . ' In the 
village of S — , near Hastings, there lived a couple 
who had named their first-born girl Helen. The 
child sickened and died, and when another daughter 



268 THE LOGICAL BASES OF EDUCATION 

was born, she was named after her dead sister. 
But she also died, and on the birth of a third 
daughter the cherished name was repeated. This 
third Helen died, "and no wonder," the neighbours 
said ; "it was because the parents had used the 
first child's name for the others." ' " — Clodd, Tom 
Tit Tot, p. 137. 

15. "In all unhealthy countries the greatest risk 
[of fever] is run by sleeping on shore. Is this 
owing to the state of the body during sleep, or to a 
greater abundance of miasma at such times 1 It 
appears certain that those who stay on board a 
vessel, though anchored at only a short distance 
from the coast, generally suffer less than those 
actually on shore." — Darwin, Journal of Voyage of 
H.M.S. Beagle, p. 441. 

16. "I find that a certain plant always grows 
luxuriantly on a particular kind of soil; if my 
experience of the other conditions be sufficiently 
various, I am justified in concluding that the soil 
probably possesses certain chemical constituents 
which are peculiarly favourable to the production of 
the plant." — Fowler, Inductive Logic, p. 139. 

17. "Publius Nigidius Figulus [was] a Roman of 
the time of Julius Caesar whom Lucan mentions as a 
celebrated astrologer. It is said, that when an 
opponent of the art urged as an objection the 
different fates of persons born in two successive 
instants, Nigidius bade him make two contiguous 
marks on a potter's wheel, which was revolving 
rapidly near them. On stopping the wheel, the two 
marks were found to be really far removed from each 
other." — Whewell, History of the Inductive Sciences, 
vol. i., p. 226. 

18. "The only proof capable of being given that 
an object is visible, is that people actually see it. 



EXERCISES 269 

The only proof that a sound is audible, is that people 
hear it : and so of the other sources of our experience. 
In like manner, I apprehend, the sole evidence it is 
possible to produce that anything is desirable, is 
that people do actually desire it." — Mill, Utili- 
tarianism, pp. 52-3. 

1 9. " Scheiner [one of the discoverers of the spots 
on the sun] was a monk ; and on communicating to 
the superior of his order the account of the spots, 
received in reply from that learned father a solemn 
admonition against such heretical notions : — ' I have 
searched through Aristotle,' he said, ' and can find 
nothing of the kind mentioned : be assured, there- 
fore, that it is a deception of your senses, or of your 
glasses.' " — Baden Powell, History of Natural 
Philosophy, p. 171. 

20. "When the palace of Nicomedia, and even 
the bedchamber of Diocletian, having been on fire 
twice within fifteen days, the people entirely refused 
to believe that it could be the result of accident." — - 
Jevons, The Principles of Science, p. 264. 

21. " A person might suppose that the peculiar 
colours of mother-of-pearl were due to the chemical 
qualities of the substance. Much trouble might 
have been spent in following out that notion by 
comparing the chemical qualities of various iridescent 
substances. But Brewster accidentally took an im- 
pression from a piece of mother-of-pearl in a cement 
of resin and bees'-Avax, and finding the colours 
repeated upon the surface of the wax, he proceeded 
to take other impressions in balsam, fusible metal, 
lead, gum arable, isinglass, &c., and always found 
the iridescent colours the same. He thus proved 
that the chemical nature of the substance is a matter 
of indifference, and that the form of the surface is 



270 THE LOGICAL BASES OF EDUCATION 

the real condition of such colours." — Jevons, The 
Principles of Science, p. 419. 

22. " Aristotle, the greatest naturalist of Greece, 
had observed that it was a curious fact, that on the 
sea-shore no animal ever dies except during the 
ebbing of the tide. Several centuries later, Pliny, 
the greatest naturalist of an empire that was washed 
by many tidal seas, directed his attention to this 
statement. He declared that, after careful observa- 
tions which had been made in Gaul, it had been 
found to be inaccurate, for what Aristotle stated of 
all animals, was in fact only true of man. It was 
in 1727 and the two following years, that scientific 
observations made at Rochefort and at Brest finally 
dissipated the delusion." — Lecky, History of European 
Morals, vol. i., p. 394. 

23. " Baron Zach received a letter from Pons, a 
successful finder of comets, complaining that for a 
certain period he had found no comets, though he 
had searched diligently. Zach, a man of much sly 
humour, told him that no spots had been seen on 
the sun for about the same time — which was true= — • 
and assured him that when the spots came back, 
the comets would come with them. Some time 
after he got a letter from Pons, who informed him, 
with great satisfaction, that he was quite right, that 
very large spots had appeared on the sun, and that 
he had found a fine comet soon after." — De 
Morgan, Budget of Paradoxes, p. 279. 

24. "No reason can be given why the general 
happiness is desirable, except that each person, so 
far as he believes it to be attainable, desires his own 
happiness. This, however, being a fact, we have 
not only all the proof which the case admits of, but 
all which it is possible to require, that happiness is a 



EXERCISES 271 

good : that each person's happiness is a good to that 
person, and the general happiness, therefore, a good 
to the aggregate of all persons." — Mill, Utilitarian- 
ism^ p. 53. 

25. ^''Nature is uniforiin in all its ojjerations. 
For instance, the production of all birds, and, 
indeed, of all living creatures, resembles that of any 
single bird which you may choose. It is only in 
the minor details that there are differences .... 

Differences of method, therefore, confuse the 
young, and make their studies distasteful to them . . . 

Henceforth, therefore, 

(i) The same method of instruction must be used 
for all the sciences, the same for all the arts, and 
the same for all languages. 

(ii) In each school the same arrangement and 
treatment should be adopted for all studies. 

(iii) The class-books for each subject should, as 
far as is possible, be of the same edition." — Comenius, 
The Great Didactic, tr. Keatinge, pp. 292-3. 

26. " Pigeons and doves offer a very curious case 
of the protection of exposed eggs. They usually 
build very slight and loose nests of sticks and twigs, 
so open that light can be seen through them from 
below, while they are generally well concealed by 
foliage above. Their eggs are white and shining; 
yet it is a difficult matter to discover, from beneath, 
whether there are eggs in the nest or not, while they 
are well hidden by the thick foliage above. The 
Australian podargi — huge goatsuckers — build very 
similar nests, and their white eggs are protected in 
the same manner. Some large and powerful birds, 
as the swans, herons, pelicans, cormorants, and storks, 
lay white eggs in open nests ; but they keep careful 
watch over them, and are able to drive away intru- 
ders. On the whole, then, we see that, while white 



272 THE LOGICAL BASES OF EDUCATION 

eggs are conspicuous, and therefore especially liable 
to attack by egg-eating animals, they are concealed 
from observation in many and various ways. "We 
may, therefore, assume that, in cases where there 
seems to be no such concealment, we are too ignorant 
of the whole of the conditions to form a correct 
judgment." — Wallace, Darwinism, pp. 213-4. 

27. "In a given state of society a certain number 
of persons (about 250 each year) must put an end 
to their own life. This is the general law, and the 
special question as to who shall commit the crime 
depends of course upon special laws, which, however, in 
their' total action, must obey the large social law to 
which they are all subordinate. And the power of 
the larger law is so irresistible, that neither the love 
of life, nor the fear of another world, can avail any- 
thing towards even checking its operation." — Buckle, 
History of Civilization, vol. i., p. 25. 

28. " Some species of fresh- water shells have very 
wide ranges, and allied species which, on our theory, 
are descended from a common parent, and must have 
proceeded from a single source, prevail throughout 
the world. Their distribution at first perplexed me 
much, as their ova are not likely to be transported 
by birds ; and the ova, as well as the adults, are im- 
mediately killed by sea-water. I could not even 
understand how some naturalized species have spread 
rapidly throughout the same country. But two facts, 
which I have observed — and many others no doubt 
will be discovered — throw some light on this sub- 
ject. When ducks suddenly emerge from a pond 
covered with duck-weed, I have twice seen these 
little plants adhering to their backs ; and it has hap- 
pened to me, in removing a little duck-weed from 
one aquarium to another, that I have unintentionally 
stocked the one with fresh-water shells from the 



EXERCISES 273 

other. But another agency is perhaps more effectual : 
I suspended the feet of a duck in an aquarium, where 
many ova of fresh-water shells were hatching ; and 
I found that numbers of the extremely minute and 
just-hatched shells crawled on the feet, and clung to 
them so firmly that when taken out of the water 
they could not be jarred off, though at a somewhat 
more advanced age they would voluntarily drop off. 
These just-hatched molluscs, though aquatic in their 
nature, survived on the duck's feet, in damp air, from 
twelve to twenty hours ; and in this length of time a 
duck or heron might fly at least six or seven hundred 
miles, and if blown across the sea to an oceanic 
island, or to any other distant point, would be sure 
to alight on a pool or rivulet. Sir Charles Lyell 
informs me that a Dytiscus has been caught with an 
Ancylus (a fresh-water shell like a limpet) firmly 
adhering to it ; and a water-beetle of the same family, 
a Colymbetes, once flew on board the Beagle, when 
forty-five miles distant from the nearest land ; how 
much farther it might have been blown by a favour- 
ing gale no one can tell." — Darwin, Origin of Species, 
pp. 344-5. 

29. " Covetousness . . . being the root of all 
evil, should be early and carefully weeded out, and the 
contrary quality of a readiness to impart to others 
implanted. This should be encouraged by great 
commendation and credit, and constantly taking care 
that [the child] loses nothing by his liberality. Let all 
the instances he gives of such freeness be always 
repaid, and with interest ; and let him sensibly per- 
ceive that the kindness he shows to others is no ill 
husbandry for himself, but that it brings a return 
of kindness both from those that receive it and those 
who look on." — Locke, Some Thoughts concer7iing 
Education, § 110. ' 

T 



274 THE LOGICAL BASES OF EDUCATION 

30. "If any one doubts the importance of an 
acquaintance with the principles of physiology, as a 
means to complete living, let him look around and 
see how many men and women he can find in middle 
or later life who are thoroughly well. . . . We 
infer that as vigorous health and its accompanying 
high spirits are larger elements of happiness than 
any other things whatever, the teaching how to 
maintain them is a teaching that yields in moment 
to none other whatever. And therefore we assert 
that such a course of physiology as is needful for 
the comprehension of its general truths, and their 
bearings on daily conduct, is an all-essential part 
of a rational education." — H. Spencer, Education, 
pp. 13, 15. 

31. "That it enables a child to control its func- 
tions, and that it will be useful in after life as a 
groundwork for household medicine, are two reasons 
for teaching physiology which might, until examined, 
have been supposed to carry weight. The first we 
disallow on the ground that it is more dangerous to 
call attention to the functions of the body than to 
let them have play unobserved, while, so far as the 
second reason goes, we believe that medical treat- 
ment is best left to the doctors." — Dr. A. Hill, 
^Physiology,' in Aims and Practice of Teaching, 
edited by Prof. F. Spencer, p. 278. 

32. "Grey, in 1729, discovered the properties of 
conductors. He found that the attraction and 
repulsion which appear in electric bodies are ex- 
hibited also by other bodies in contact with the 
electric. In this manner he found that an ivory 
ball, connected with a glass tube by a stick, a wire, 
or a packthread, attracted and repelled a feather, as 
the glass itself would have done. He was then led 
to try to extend this communication to considerable 



EXERCISES 275 

distances, first by ascending to an upper window 

and hanging down his ball, and afterwards, by 

carrying the string horizontally supported on loops. 

As his success was complete in the former case, he 

was perplexed by failure in the latter ; but when he 

supported the string by loops of silk instead of 

hempen cords, he found it again become a conductor 

of electricity. This he ascribed at first to the 

smaller thickness of the silk ; which did not carry 

off so much of the electric virtue ; but from this 

explanation he was again driven, by finding that 

wires of brass still thinner than the silk destroyed 

the effect. Thus Grey perceived that the efficacy of 

the support depended on its being silk, and he soon 

found other substances which answered the same 

purpose. The difference, in fact, depended on the 

supporting substance being electric, and therefore 

not itself a conductor ; for it soon appeared from 

such experiments, and especially from those made 

by Dufay, that substances might be divided into 

electrics per se, and non-electrics, or conductors. 

These terms were introduced by DesaguHers, and 

gave a permanent currency to the results of the 

labours of Grey and others." — Whewell, History of 

the Inductive Sciences, vol. iii., p. 9. 

33. " The pubKcation of the quartos in 1609 gives 
us one limit for the date of Troilus and Cressida, hut 
(i) certain discrepancies in the text, (ii) differences of 
style, thought, language, and metrical qualities, and 
(iii) important pieces of external evidence, make it 
almost certain that the play passed through various 
stages of revision, and was in all probability com- 
posed at different times." — GoUancz, Introd. to 
Troilus and Cressida, Temple Ed. 

34. "Locke's great maxim was that we ought 
to reason with children. . . . Reason, apparently 



276 THE LOGICAL BASES OF EDUCATION 

a compound of all other faculties, the one latest 
developed, and with most difficulty, is the one pro- 
posed as agent in unfolding the faculties earliest 
used ! The noblest work of education is to make a 
reasoning man, and we expect to train a young child 
by making him reason ! This is beginning at the 
end ; this is making an instrument of a result. If 
children understood how to reason they would not 
need to be educated." — Rousseau, :^mile (Steeg's 
Extracts translated by Worthington), p. 52. 

35. "The most generally received theory [as to 
the origin of animal coloration] undoubtedly is that 
brilliancy and variety of colour are due to the direct 
action of light and heat ; a theory no doubt derived 
from the abundance of bright-coloured birds, insects, 
and flowers which are brought from tropical regions. 
There are, however, two strong arguments against 
this theory. . . . Bright coloration is wanting in 
desert animals, yet here heat and light are both 
at a maximum, and if these alone were the agents 
in the production of colour, desert animals should be 
the most brilliant. Again, all naturalists who have 
lived in tropical regions know that the proportion of 
bright to dull coloured species is little if any greater 
there than in the temperate zone, while there are 
many tropical groups in which bright colours are 
almost entirely unknown. . . . Again, there are 
many families of birds which spread over the whole 
world, temperate and tropical, and among these 
the tropical species rarely present any exceptional 
brilliancy of colour. . . . The same general facts 
are found to prevail among insects. Although 
tropical insects present some of the most gorgeous 
coloration in the whole realm of nature, yet there 
are thousands and tens of thousands of species which 
are as dull coloured as any in our cloudy land. 



EXERCISES 277 

. . . The various facts which have now been briefly 
noticed are sufficient to indicate that the light 
and heat of the sun are not the direct causes of the 
colours of animals, although they may favour the 
production of colour, when, as in tropical regions, the 
persistent high temperature favours the development 
of the maximum of life." — ^ Wallace, Darwinism, pp. 
193-5. 

36. " It may be laid down as a fundamental pro- 
position that a wise nation will not subsidize insti- 
tutions which might be self-supporting. . . . All 
instruction which is obviously conducive to eventually 
earning money can be left to take care of itself; 
there is no occasion whatever to subsidize technical 
instruction, except so far as capital expenditure is 
concerned, in any sense of the phrase, because as 
soon as any proficiency is seen to be likely to earn 
money, people will willingly pay to enable their 
children to acquire it." " So long as there are skilled 
workmen to be found, it is of no advantage to the 
State that they should be the children of persons 
who could not afibrd, or were unwilling to pay for 
their instruction." — Tarver, The Dehateable Land, pp. 
64, 73, 71. 

37. "At Erith, in 1864, there occurred a tremen- 
dous explosion of a powder magazine. The village 
of Erith was some miles distant from the magazine, 
but in nearly all cases the windows were shattered ; 
and it was noticeable that the windows turned away 
from the origin of the explosion suffered almost as 
much as those which faced it. Lead sashes were 
employed in Erith church ; and these, being in some 
degree flexible, enabled the windows to yield to pres- 
sure without much fracture of glass. Every window in 
the church, front and back, was bent inwards. In fact, 
as the sound-wave reached the church, it separated 



278 THE LOGICAL BASES OF EDUCATION 

right and left, and, for a moment, the edifice was clasped 
by a girdle of intensely compressed air, which forced 
all its windows inwards. After compression, the air in 
the church no doubt dilated, and tended to restore 
the windows to their first condition. The bending in 
of the windows, however, produced but a small con- 
densation of the whole mass of air within the 
church ; the force of the recoil was, therefore, feeble 
in comparison with the force of impact, and insufO.- 
cient to undo what the latter had accomplished." — 
Tyndall, On Sound, p. 23. 

38. "By our various physical sensations and de- 
sires, Nature has insured a tolerable conformity to 
the chief requirements. Fortunately for us, want of 
food, great heat, extreme cold, produce promptings 
too peremptory to be disregarded. And would men 
habitually obey these and all like promptings when 
less strong, comparatively few evils would arise. If 
fatigue of body or brain were in every case followed 
by desistance ; if the oppression produced by a close 
atmosphere always led to ventilation ; if there were 
no eating without hunger, or drinking without thirst; 
then would the system be but seldom out of working 
order. But so profound an ignorance is there of the 
laws of life, that men do not even know that their 
sensations are their natural guides, and (when not 
rendered morbid by long-continued disobedience) 
their trustworthy guides. So that though, to speak 
teleologically, Nature has provided efficient safe- 
guards to health, lack of knowledge makes them in 
a great measure useless." — H. Spencer, Ediication, 
p. 13. 

39. " When a child falls, or runs its head against 
the table, it suffers a pain, the remembrance of which 
tends to make it more careful. ... If it lays hold 
of the fire-bars, thrusts its hand into a candle-flame, 



EXERCISES 279 

or spills boiling water on any part of its skin, the 
resulting burn or scald is a lesson not easily for- 
gotten. . . . Now in these cases, Nature illustrates 
to us in the simplest way, the true theory and prac- 
tice of moral discipline. . . . Observe, first, that in 
bodily injuries and their penalties we have misconduct 
and its consequences reduced to their simplest forms. 
Though, according to their popular acceptation, right 
and wrong are words scarcely applicable to actions 
that have none but direct bodily effects ; yet whoever 
considers the matter will see that such actions must 
be as much classifiable under these heads as any other 
actions. . . . Note, in the second place, the charac- 
ter of the punishments by which these physical trans- 
gressions are prevented. > . . They are not artificial 
and unnecessary inflictions of pain j but are simply 
the beneficent checks to actions that are essentially 
at variance with bodily welfare — checks in the ab- 
sence of which life would be quickly destroyed by 
bodily injuries. . . . Let it be further borne in 
mind that these painful reactions are proportionate 
to the transgressions. . . . And then mark, lastly, 
that these natural reactions which follow the child's 
wrong actions, are constant, direct, unhesitating, and 
net to be escaped. . . . Have we not here, then, 
the guiding principle of moral education ? . . . No 
unprejudiced reader will hesitate in his assent." — 
H. Spencer, Education, pp. 101—5. 

40. " Rousseau thought it was best to let children 
incur the natural consequences of their actions. 
Spencer has reproduced the same theory under the 
name of natural reactions. . . . Spencer's principle 
has been often criticized, and not unjustly. . . . 
Suppose a boy is simply inattentive during the lesson. 
The master cannot reprove him without infringing 
the doctrine of natural reactions. But if a boy is 



280 THE LOGICAL BASES OF EDUCATION 

inattentive one day, and is made to suffer no incon- 
venience, he will be inattentive the next and the 
following days. A bad habit is quickly contracted, 
and the natural reaction is only produced when the 
evil is irreparable. Inattention and habitual care- 
lessness in a boy are naturally followed by ignorance, 
intellectual inferiority to his hard-working school- 
fellows, and finally by the difficulties of life resulting 
from that inferiority. The injury is only felt a long 
time after the faults of school-life, but then it is 
irreparable. . . . The child who neglects his work 
and plays till he is tired will not feel the punishment 
of his moral fault by physical fatigue. , . . Cold 
water is agreeable when one is bathed in perspira- 
tion; the natural reaction is inflammation of the 
lungs. Are we to wait till it comes 1 In a word, a 
man left to the mercy of natural reactions would 
descend in the animal scale ; he would not even 
live. . . . Spencer may ... be reasonably blamed 
for calling the system of discipline by natural conse- 
quences moral education. These reactions only teach 
the children the relations of natural causality (and 
that, too, not always with sufiicient emphasis), but 
they are not of a moral character." — Guyau, Educa- 
tion and Heredity, pp. 188-96. 



INDEX 



' Abstract,' meaning of, 65 
' Accidentaroccurrences,177- 

178 
' Accidents,' 224 
Accuracy in testimony, 158 — 

160 
Agreement, method of, 188 — 

191 
Ambiguity in construction of 

sentences, 60 — 61 

in words, 55 — 59 

Analogy and hypotheses, 171 ; 

180—184 

and syllogism, 180 

importance of resem- 
blances in, 181—183 
Analysis and synthesis, 73 — 75; 

121—122 
Anonymous testimony, 160 — 

162 
Aristotle and method, 101 
on induction and science, 

136—137 
Arithmetical constructions, 

133—135 
Armstrong 

methods, 256 
Atoms, 15—16 



on heuristic 

258 



Bacon and method of know- 
ledge, 106—107 

■ — ■ — on induction by simple 
enumeration, 180 

on the method of know- 
ledge, 107 

Bain, example of method of 
agreement, 188 — 189 

Ball, example of working hypo- 
thesis, 172 

on Kepler's laws and 

gravitation, 215 



Ball, on Ptolemaic hypothesis, 

172; 173—4 
Belief and judgment, 70 — 71 

compared with knowledge, 

4—7 

nature of, 4 ; 5 — 6 

Bias and hypotheses, 170 — 171 
Biology, method in, 208 
Bosanquet on beginnings of ex- 
perience, 28 

on conversion by limita- 
tion, 100 

on copula, 77 

on development of ideas, 

45 

on evidence for clairvoy- 
ance, 156 

on experiment, 151 

on form and matter, 65 — 

66 

on hypothesis and deduc- 
tion, 138 

on individual construc- 
tions of world, 25 

on induction and deduc- 
tion, 120 

on logical and grammatical 

subject, 76—77 
on meaning of proper 

names, 231 

on meanings of words, 55 

on need of decision in 

practical matters, 156 

on truth of hypothetical 

judgments, 87 

Bradley on analysis and syn- 
thesis, 121 ; 122 

• on inference from rela- 
tions, 132—133 

Bryant on arithmetical units, 
133 



282 



INDEX 



Bryant on arrest of develop- 
ment, 264 

on docility in learning, 

260 

on true development, 247 

—248 

Burlce on analogy between 
man and nation, 182 

Causal and casual sequences, 

177—178 
Causation and sequence in 

time, 36-38 

axioms of, 33 — 36 

uniformity of, 14 ; 32 — 

36 
Cause and effect, 16 ; 34 — 36 ; 

38 

efficient, 33 

final, 39-41 

Causes, plurality of, 34 — 36 
Change, nature of, 12 — 14 ; 16 
Circumstantial evidence, 206 — 

207 
Classification and evolution, 

239—242 
and explanation, 242 — 

244 

' and partition, 237-238 

connexion with definition, 

221 ; 235—237 

disjunctive, 238 

nature of, 234—235 ; 237 

—238 ; 241—242 

origin of, 221 

rules of, 235 

• subsumptive, 238—241 

Clifford on establishment of 

hypotheses, 204 

on explanation, 245 

■ on precision of scientific 

law, 198 

on science, 15 

Clodd on superstition, 2; 3 ; 

4; 10; 11; 143 
Coleridge on the nature of 

method, 108 
on parallelism in develop- 
ment of child and race, 250 



Coleridge on true and false 
education, 252—253 ; 258— 
259 

Colour of animals, investiga- 
tion of, 200—203 

Comenius on education accord- 
ing to nature, 57 

Concomitant variations, 
method of, 195—199 

' Coiicrete,' meaning of, 65 

Conduct influenced by super- 
stition, 4 

Connotation, 225 

Conservation of energy, 
15-16 

Constructive inference, 
123—124 ; 132—135 

Content, 98 ; 227 

Contradiction of propositions, 
102 

principle of, 29—30 ; 31 ; 

39 

Contrariety, 102 

Cojiversionof propositions, 99 — 
101 

Copula, 77—78 

Cross-examination, 162 — 163 

Crucial instance, 174 — 176 

Darwin, example of Method of 
Exclusions, 196 

on genealogical classifica- 
tion, 239—240 

Decle on savage view of causa- 
tion, 33 

Definition and meaning, 226 — 
231 

connexion with classifica- 
tion, 221 ; 235—237 

function of, 223; 226— 

229 

nature of, 223—226; 241— 

242 

origin of, 221—222 

rules of, 231—234 

De Morgan on Digby's sympa- 
thetic powder, 143 

on illustrations, 115 

on inductive method, 137 



INDEX 



283 



De Morgan on origin of hypo- 
theses, 167 

on ' publication,' 55 — 56 

Denotation, 98 ; 227 

Descriptive hypotheses, 172 

Development of knowledge, 
stages of, 9—26 ; 81 

Difference, method of, 192 — 
195 

Distribution of terms, 98 — 99 

Dogmatism in education, 260 

' Education according to Na- 
ture,' 57—58 
and individuality, 253 — 

255 
relation of logic to, 246 — 

249 
relative to society, 249 — 

252 
Educational method, maxims 

of, 261—265 
Empirical laws, 204 
Energy, 15—16 
Enumerative induction, 178 — 

180 
Erdmann on copula, 77 
Event, nature of, 16 ; 38 
Evidence, circumstantial, 206 

—207 

negative, 164—165 

Evolution and classification, 

239—242 
Excluded middle, principle of, 

30—31 ; 39 
Exclusions, method of, 191 — 

192 
Experiment, crucial, 174—176 

nature of, 150—152 

Explanation and classification, 

242-244 

limits of, 244 

nature of, 244—245 

of world, stages of, 9—26 ; 

29—41 ; 81—94 

Fact, expression of, 81—85 

nature of, 71 — 72 

Factors of change, 12 — 14 



Facts and hypotheses, 168 — 

170 
and method of knowledge, 

109 
Fallacy and ambiguity of lan- 
guage, 61 

definition of, 112 

ignoratio elenchi, 114 — 

115 

illicit conversion, 100 

illicit process, 127—128 

liability of illustrations 

to, 115 

petitio principii, 112 — 114 

undistributed middle, 

124—127 
Falsity and falsehood, 70 — 71 
Femer on development of 

knowledge of language, 51 
on logic and reasoning, 

67 
Figures of syllogism, 129 — 130 
Form and matter, 65 — 66 

Generalization, influence of 

language in, 178 — 179 
' Genus,' 235 

Geology, method in, 208—213 
Geometrical constructions, 135 
Gestures in language, 46 — 47 
Good faith in testimony, 156 — 

158 
Gravitation, establishment of 
theory, 213—219 

Harris on arrest of develop- 
ment, 264 

on development of know- 
ledge, 40—41 

on thinking and imaging, 

43 

Herschel, example of false per- 
ception, 141 

on necessity of knowledge 

to observation, 142 

on Newton's experiment 

with pendulums, 213 — 214 

on numerical precision in 

science, 198 



284 



INDEX 



Herschel on object of science, 
167 

statement of undulatory 

theory of light, 175 

Heuristic methods, 255 — 257 
Hihhen, example of limitation 

of concomitant variations, 

199 
on dependence of inference 

on system, 118 
History, method in, 207—208 
Hohhes, definition of 'name,' 

232—233 
Hobhouse, example of circmn- 

stantial evidence, 206 

example of method of 

concomitant variations, 197 

on abstract nature of 

thought, 64 

on completion of science, 

244 

on confusion of observa- 
tion and inference, 147 

on conversion, 100 — 101 

on distinction between 

subject and predicate, 76 

on explanation, 244 

on isolated words, 52 

on limitations of method 

of agreement, 190 
on logic and reasoning, 68 

on meaning of proper 

names, 231 

on nature of numbers, 134 

on plurality of causes, 

35—36 

on quasi-inductive charac- 
ter of early mathematics, 135 

on separability of events, 

38 

on subject-matter of logic, 

66—67 

on work of science, 170 

Huxley on universality of law, 
14 

Hypotheses and analogy, 171 ; 
180—184 

and bias, 170—171 

and facts, 168—170 



Hypotheses, descriptive, 172 

nature of, 166—167; 184— 

185 

origin of, 167—168 

■ permissible, 173—174 

— testing of, 138—139 ; 171 
working, 172—173 

Ideas and images, 43 — 44 

and knowledge, 42 

and language, 45 — 46 

and reality, 42 — 43 

■ development of, 45 

Identity, principle of, 29 ; 31 ; 

39 
Ignoratio elenchi, 114 — 115 
Illicit conversion, 100 

process, 127—128 

Induction, enumerative, 178 — 
180 

general method of, 137 — 

138 

meaning of, 136 — 137 

Inductive methods — Agree- 
ment, 188—191 

character of, 184—187 

Concomitant Variations, 

J95 199 

Difference, 192—195 

example of, 200—203 

Exclusions, 191—192 

principles underlying, 186 

—187 

Residues, 200 

Indirect method in induction, 

scope of, 204—206 
Inference and method of know- 
ledge, 110—111 

and observation, 142 — 149 

and system, 117 — 118 

constructive, 123 — 124 ; 

132—135 
logical and psychologi- 
cal, 116—117 

nature of, 116 — 119 

relation of deduction 

and induction, 119 — 122 

relative to previous 

knowledge, 118—119 



INDEX 



285 



Inference, subsumptive, 123 ; 
124—132 

syllogistic, 123 ; 124—132 

universals in, 119 

Jacotot on method in teaching, 

254 
James on limitations of popular 

knowledge, 228 
Jevons on Bacon's method of 

knowledge, 106 
on bias in observation, 

170 
on crucial experiment in 

light, 175—176 
on theory of gravitation, 

218—219 
Judgment and belief, 70—71 

and experience, 72 — 73 

and proposition, 69 — 70 ; 

76—77 

and reality, 72 — 73 

and sentence, 71 

aftd truth, 70—72 

both analytic and synthe- 
tic, 73—75 ; 78 

categorical, 81 — 85 

demonstrative, 82 

development of, 81 — 91 

disjunctive, 81; 88—91 

enumerative, 83 

forms of, relative to stages 

of knowledge, 81 
• fundamental questions 

about, 63 

generic, 85 

■ grounds of, 72 

historical singular, 83 

hypothetical, 81 ; 85—88 

impersonal, 81 — 82 

nature of, 63; 69—79 

negative, 92 — 94 

particular, 84 ; 94—96 

■ parts of, 75—78 

of particular relation, 82— 

83 
quality and quantity in, 

94—96 
reception of, 70 



Judgment, reciprocal uni- 
versal, 88 
search for universal, 84 — 

85 

Kendall, example of induction 
in geology, 209 — 213 passim 
Knowledge and belief, 4 — 7 

and education, 1 

and ideas, 42 

and logic, 62—63 

and reality, 19 — 26 

and superstition, 2 — 4 

definition of, 2 

factors of, 27 

nature of, 2 ; 5—6 ; 19—24 

postulates of, 28 — 39 

stages of, 9—26 ; 81 

Langlois and Seignohos on 
chronic inaccuracy, 159 

on detail in testimony, 

157—158 

on identical errors in 

documents, 161 — 162 

on method of history, 207 

on method of knowledge, 

112 
on 'the accent of sincerity,' 

157 
Language and ideas, 45 — 46 

and learning, 48 — 49 

influenceongeneralization, 

178—179 

influence on thought, 61 

nature of, 45 — 46 

— verbal, 46—47 ; 49—50 

written, 47 ; 49—50 

Law, expression of, 81 ; 85 — 88 
meaning of, 138 

necessary character of, 

14—15 
Laws, empirical, 204 
Logic and judgment, 63 — 64 

and knowledge, 62 — 63 

■ definition of, 63 

function of, 67—68 

general relation to educa- 
tion, 246—249 



286 



INDEX 



Logic, mediseval, aim of, 67 ; 

105—106 
modern, aim of, 67 — 68 ; 

108 

nature of, 62—63; 64; 

66—67 

value of, 68 

Lotze on atoms, 15 

Mach on cause and effect, 16 

■ on explanation, 33 

Maxims of educational method, 

261—265 
Meaning, ambiguities in, 55 — 

61 

and definition, 226—231 

general and specific, 53 — 

55 
influenced by context, 

50—53 
Mediseval logic, aim of, 67 ; 

105—106 
Memory, untrustworthiness of 

160 
Merz, examples of descriptive 

hypotheses, 172 ; 173 
on limitations of science, 

17 
Method, analytic and synthetic, 

121—122 

and facts, 109 

and inference, 110 — 111 

and self -activity, 108 — 

109 ; 252—253 
and thought, 108—109 

252—255 
characteristics of, 111- 

112; 116 
development of doctrine, 

105—108 
educational, maxims of, 

261—265 

fallacies in, 112 — 115 

heuristic, 255—257 

in education and in science, 

257—261 

in education relative to 

conception of knowledge, 
255 



Method, nature of, 104—105 ; 
108—109; 110—112; 116 ; 
258 

not mechanical, 253 — 255 

of knowledge, aim of, 

220—221 

Methodical process, character- 
istics of, 111—112; 116 

Methods and subjects of study, 
258—257 

Hill and method of knowledge, 
107 

on plurality of causes, 35 

on variety of nature, 32 

Minto on Bacon's method of 
knowledge, 106 

Modern logic, aim of, 67 — 68 ; 
108 

Morgan, example of con- 
struction of ideas, 48 — 49 

example of explanation, 

243—244 

Negation, 91—94 
Negative evidence, 164 — 165 
Newton and method of know- 
ledge, 107 
Niebuhr on legends, 164 

Observation and inference, 

142—149 

and prejudice, 149 — 150 

importance of, 109 ; 140 

influence of knowledge 

in, 141—142 

liability to error, 140 — 141 

selection of matter in, 

142—143 
Opposition of propositions, 

101—103 

Parallelism between de- 
velopment of child and 
race, 250—252 

Partition and classification, 
237—238 

Pestalozzi on foundations of 
instruction, 257 

on method in instruction, 

253 ; 254 



INDEX 



287 



Petitio principii, 112 — 114 
Plato on written and verbal 

language, 50 
Predicate and subject, 75 — 77 
Prejudice and observation, 

149—150 
Proper names, meaning of, 

230—231 
' Properties,' 223—224 
Propositions and judgments. 

69—70 ; 76—77 

and sentences, 71 

concrete conditional, 87 — 

88 

conversion of, 99 — 101 

• four-fold scheme of, 97 — 

98 

negative, 92 — 94 

opposition of, 101 — 103 

particular, 84 ; 94—96 

parts of, 75 — 78 

universal categorical, 85 

'Pure case,' 169 

Ravenshear on corroboration of 

testimony, 164 

on expert testimony, 142 

on necessity of testimony, 

109 ; 153 
Read, example of crucial 

instance, 174 
• example of method of 

exclusions, 191 
on causation and classifi- 
cation, 241 
on explanation and 

familiarization, 244 — 245 
on indirect induction, 

138—139 
• on temporary character 

of classification, 242 
on vagueness of popular 

language, 226—227 
Reality and judgment, 72 — 73 

and knowledge, 19 — 26 

Recognition, 143 — 147 
Residues, method of, 200 
Rooper, example of invalid 

perception, 92 



Rushin on effect of modern 
education, 249 

Savage philosophy, 7—9 
Savages, language of, 46 — 47 
Scientific instruments, 150 
Selection of matter in observa- 
tion, 142—143 
Sense-experience, limitations 

of, 20—21 
Sense-perception and syllogism, 

143—147 
Sentence and judgment, 71 
' Some,' meaning of, 94 — 95 
'Species,' 235 

Spencer, examples of fallacies, 
113 — 115 passim, 

on parallelism of de- 
velopment in child and race, 
250 

Stages of explanation of world, 

9—26 ; 29—41 ; 81—94 
Stirling on images and thought, 

43-44 
Stoclc, example of ambiguity, 

60 

on ignoratio elenchi, 114 

Subalternation, 101—102 
Sub-contrariety, 103 
Subject and predicate, 75 — 77 
Subsumptive inference, 123 ; 

124—132 
Sufficient Reason, principle of, 

31 ; 32—38 ; 39 
Superstition and conduct, 4 

and knowledge, 2 — 4 

Swinburne on copula, 77 
Syllogism and analogy, 180 

and enumerative in- 
duction, 179 

and sense-perception, 

143—147 

Aristotle's definition of, 

124 

categorical, 124 — 130 

figures of, 129—130 

hypothetical, 130—132 

— nature of inference in, 

123 ; 125—126 ; 128—129 



288 



INDEX 



Syllogism, not a petitio prin- 

cipii, 128 
rules of, 124—128 ; 129 ; 

131 
Synthesis and analysis, 73 — 75 ; 

121—122 
System, expression of, 89 — 91 
nature of, 17 — 18 

Teaching, function of, 1 
Tennyson quoted, 12 ; 19 
Terms, distribution of, 98—99 
Testimony, accuracy in, 158 — 

160 

anonymous, 160 — 162 

corroboration of , 162 — 164 

good faith in, 156 — 158 

■ ■ necessity of, 109 ; 153 — 

154 

reception of, 154 — 155 

tests of, 155—160 

'Theory,' meaning of, 138 
Thompson, example of analogy, 

183—184 
Thomson mid Tait on graphic 

expression of variation, 198 — 

199 
Thought, abstract nature of, 

64—65 
and method of knowledge, 

108—109 

function of, 20—24 

■ influenced by language, 61 

Tradition, 163—164 
Truth and evidence, 104 

and judgment, 70 — 72 

test of, 23—24 

Turgot on mental indolence, 5 

Undistributed middle, 124— 
127 



Universe, as governed by law, 

11—16; 31—38 
as mental construction, 

24—26 
as sum of things, 9 — 11 ; 

29—31 

as system, 16 — 19 ; 24 ; 

38—41 

Venn on beginnings of classifi- 
cation, 221 

on definition and meaning, 

229 

on dependence of defini- 
tion on knowledge, 225 

on difficulty of experi- 
ment, 193—194; 194—195 

on nature of inductive 

methods, 185 

Wallace, example of method of 
concomitant variations, 196 
—197 

example of mistaken 

analogy, 182—183 

investigations in colour of 

animals, 200 — 203 passim 

on evolution and classifi- 
cation, 243 

Whewell on cause and effect in 
time, 37 

on common errors in ob- 
servation, 141 

on development of theory 

of gravitation, 216 — 218 
passim 

on principle of causation, 

38 

Working hypotheses, 172—173 



Xenophon on enquiries 
Socrates, 222 



of 



K. CLAY AND SONS, LTD., BREAD ST. HILL, E.G., AND BUNGAY, SUFFOLK. 



Macmillan's 
Manuals for Teachers 



EDITED BY 

OSCAR BROWNING, M.A., 

PRINCIPAL OF THE CAMBRIDGE UNIVERSITY DAY TRAINING COLLEGE, 
AND 

S. S. F. FLETCHER, M.A., Ph.D., 

MASTER OF METHOD IN THE CAMBRIDGE UNIVERSITY DAY TRAINING COLLEtJE. 

PRINCIPLES OF CLASS TEACHING. By 

J. FiNDLAY, M.A., Professor of Education in Victoria 
University, Manchester. 5^. [Ready. 

SCHOOL MANAGEMENT. By George Collar, 

B.A., B.Sc, Principal of the Stockwell Pupil Teacher 
School, and C. W. Crook, B.A., B.Sc. 3^. 6d. {Ready. 

THE LOGICAL BASES OF EDUCATION. By 
James Welton, M.A., Professor of Education and 
Master of Method at the Yorkshire College, Victoria 
University. Globe 8vo, 3^. 6d. {Ready: 

Volu?nes in Preparation. 

PSYCHOLOGY FOR TEACHERS. By John 

Adams and Professor James Welton, M.A. 

HISTORY OF EDUCATION. By OsCAR 
Browning, M.A., and S. S. F. Fletcher, M.A., Ph.D. 



LONDON: MACMILLAN AND CO., Ltd. 



VOLUMES NOW READY. 

PRINCIPLES OF CLASS TEACH- 

ING. By J. J. FiNDLAY, M.A., Ph.D., Professor of 
Education in Victoria University, Manchester. 
Globe Svo., 5^". 

Tke Times. — " So full of good matter that a short notice can do little more thr.p 
indicate its main objects. . . . Probably the most truly scientific treatise on t' ; 
subject of education that our country has as yet produced." 

Mr. Spenser Wilkinson in the Morning Post. — " I know of no educational 
book which shows with equally convincing closeness of argument the connection 
between national efficiency and a national system of education. . . . The appearance 
of a book like tbis is one of the most hopeful signs for the nation's future. If the 
schoolmasters are awake the nation will in time become alert." 

Dublin Express. — "Cannot fail to be of practical benefit to teachers, old and 
young, as well as to anyone who grasps the importance of a sound system of educa- 
tion to the future of the Empire." 

THE LOGICAL BASES OF EDU- 
CATION. By J. Welton, M,A. Globe Zvo., 

Journal of Education. — " Prof. Welton writes in a clear and pleasant style, 
and the examples and illustrations which he uses to make his views fully intelligible, 
are excellently chosen. One sees very soon that he is a master of his subject. . . , 
Likely to be very useful to students. . . . We heartily recommend this book to our 
readers' attention." 

Educational Times. — "Mr. Welton has written distinctively well on logic, but 
we are inclined to think that he has never produced anything better than this succinct 
and lucid exposition of the application of logical method to educational purposes. . . . 
The volume appears in a series of ' Manuals for Teachers ' ; it will be an admirable 
series if the rest of the volumes come anywhere near the excellence of this one." 



SCHOOL MANAGEMENT AND 

METHODS OF INSTRUCTION. With 
special Reference to Elementary Schools. By 
George Collar, B.A., B.Sc and Charles W. 
Crook, B.A., B.Sc. Globe 8w., 3^-. 6d. 

Practical Teacher.— "-^ K valuable addition to the literature dealing with the 
practical side of education. . . . We recommend the book stronglv, not only to those 
members of the profession who are preparing for an examination in the subject, but 
also to all teachers who are interested in their work." 

School World. — "We heartily recommend this volume to acting teachers as well 
as to students in training." 



LONDON : MACMILLAN AND CO., Ltd. 



NOV 2 1906 








o V 




-^^ 



vT 










'^^.^'^ ' 









'^^r 






) DOBBS BROS 

LIBRARy BINDING ' I > 




Ho^ 



.•WAR 81 v'' »:i©^% «; 



♦* .♦ 



ST. AUGUSTINE t*-^ 




